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Construct Khukhro's 2-generator 7-group counterexample to the Hughes
conjecture, and then repeatedly factor out complements to [b,a]^7 in
the centre of the group, so as to obtain smaller counterexamples
B(2,7 : 13) has order 7^668
The p-covering group G has order 7^1258 and class 14
G is generated by a and b; and [b,a] has order 49
[b,a,a] has order 7 ; [b,a,b] has order 7
gamma_3(G) is the normal closure of < [b,a,a], [b,a,b] >,
and gamma_3(G) has class at most 4, so gamma_3(G) has exponent 7
Now compute suitable 7th powers of elements outside the derived group
Loading "twB27c8"
The quotient group H has order 7^1075
H is generated by a and b; and [b,a] has order 49
H is Khukhro's 2-generator anti-Hughes 7-group
Now factor out a complement for [b,a]^7 in the multiplier
Factoring out a complement of H.702 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.703 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.704 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.721 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^6
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.722 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^5
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.726 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^4
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.730 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^5
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.732 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^4
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.733 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.736 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^3
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.738 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^6
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.739 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^5
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.743 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^6
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.746 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^4
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.748 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^6
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.749 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.751 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.753 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^6
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.754 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.755 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.756 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^2
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.757 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^2
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.759 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^4
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.760 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.764 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.768 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.770 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.771 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.774 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^4
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.776 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^2
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.777 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^6
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.779 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.781 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.784 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.785 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^6
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.786 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.788 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.789 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.791 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^4
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.793 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.794 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^2
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.795 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^4
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.797 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^3
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.799 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^6
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.801 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.803 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.804 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^5
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.805 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.806 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.807 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.808 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^4
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.809 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^3
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.810 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.811 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^5
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.812 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.813 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.814 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^2
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.815 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.816 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.818 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.819 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^2
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.820 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.822 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^2
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.824 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.825 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^2
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.827 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.829 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.830 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^5
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.831 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.834 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^7
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^119
generated by a and b; and [b,a]^7 = NextQ.119^3
The centre is generated by CurrentQ.119 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^119
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.835 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.837 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.838 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.840 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.842 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.844 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.845 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.846 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^9
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^117
generated by a and b; and [b,a]^7 = NextQ.117^6
The centre is generated by CurrentQ.117 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^117
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.847 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.848 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.850 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.851 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.852 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.853 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.854 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
Z, its centre, has order 7^2
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^117
generated by a and b; and [b,a]^7 = NextQ.117^4
The centre is generated by CurrentQ.117 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^117
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.855 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.857 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.858 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.859 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.860 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^3
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.861 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.862 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.863 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.865 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.866 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.867 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.868 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.869 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.870 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.871 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.872 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.873 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^2
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.874 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^4
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.875 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.876 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.877 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.878 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^2
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.881 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.882 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.883 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.884 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.886 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.887 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^3
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.888 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.889 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.890 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.891 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.892 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.893 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.894 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.895 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.896 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.897 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.898 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.899 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.900 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.902 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.903 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.904 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.905 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.906 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.908 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.909 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.911 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.912 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.913 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.914 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.915 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.917 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.918 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.919 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.920 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.921 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.922 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.923 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.924 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.925 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.926 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.927 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.928 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.929 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.930 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.931 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.932 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.933 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.934 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.935 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.937 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.941 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.942 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.943 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.944 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.945 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.946 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.947 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.948 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.949 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.950 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.953 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.954 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.956 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.957 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.958 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.959 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.960 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.962 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^5
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.963 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.964 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.965 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.966 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.967 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.968 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.970 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.971 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.973 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.974 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.976 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.977 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.978 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.979 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.980 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.981 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.982 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.983 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.984 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.985 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.987 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.988 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.995 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.999 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^2
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1004 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^3
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1005 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1007 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1014 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1015 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1016 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1017 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1018 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^3
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1019 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^5
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1020 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^3
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1021 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1022 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^6
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^120
generated by a and b; and [b,a]^7 = NextQ.120^4
The centre is generated by CurrentQ.120 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^120
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1023 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^6
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1032 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1035 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^6
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^6
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^6
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^6
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^6
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^6
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1038 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1039 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^4
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1053 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1057 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^4
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^4
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^4
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^4
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^4
Z, its centre, has order 7^8
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^118
generated by a and b; and [b,a]^7 = NextQ.118^4
The centre is generated by CurrentQ.118 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^118
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1058 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^5
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^5
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^5
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^5
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^5
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^5
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1063 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^3
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^3
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^3
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^3
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^3
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^3
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Factoring out a complement of H.1069 gives us a smaller anti-Hughes group
CurrentQ with order 7^669
CurrentQ is generated by a and b; and [b,a]^7 = CurrentQ.669^2
Z, its centre, has order 7^259
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^411
generated by a and b; and [b,a]^7 = NextQ.411^2
Z, its centre, has order 7^156
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^256
generated by a and b; and [b,a]^7 = NextQ.256^2
Z, its centre, has order 7^87
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^170
generated by a and b; and [b,a]^7 = NextQ.170^2
Z, its centre, has order 7^46
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^125
generated by a and b; and [b,a]^7 = NextQ.125^2
Z, its centre, has order 7^5
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^121
generated by a and b; and [b,a]^7 = NextQ.121^2
The centre is generated by CurrentQ.121 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^121
which is as far as we can reduce the group (by this method!)
Total time: 7938.250 seconds, Total memory usage: 734.27MB