Magma V2.14-14 Fri Jan 02 2009 10:53:16 on havas-xps [Seed = 1096117600]
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Construct Khukhro's 3-generator 5-group counterexample to the Hughes
conjecture, and then repeatedly factor out complements to c^5 in
the centre of the group, to obtain smaller counterexamples
B(3,5 : 8) has order 5^505
The p-covering group G has order 5^1380 and class 9
G is generated by a, b and c; and c has order 25
[b,a] has order 5 ; [c,a] has order 5 ; [c,b] has order 5
gamma_2(G) is the normal closure of < [b,a], [c,a], [c,b] >,
and gamma_2(G) has class at most 4, so gamma_2(G) has exponent 5
Now compute suitable 5th powers of elements outside G'
Loading "twB35c5"
The quotient group, H, has order 5^917
H is generated by a, b and c; and c^5 = H.917
H is Khukhro's 3-generator anti-Hughes 5-group
Z, its centre, has order 5^412
Now build a complement for c^5 in Z
Factor it out to get an anti-Hughes group of order 5^506
generated by a, b and c; and c^5 = NextQ.506
Z, its centre, has order 5^238
Now build a complement for c^5 in Z
Factor it out to get an anti-Hughes group of order 5^269
generated by a, b and c; and c^5 = NextQ.269
Z, its centre, has order 5^124
Now build a complement for c^5 in Z
Factor it out to get an anti-Hughes group of order 5^146
generated by a, b and c; and c^5 = NextQ.146
Z, its centre, has order 5^45
Now build a complement for c^5 in Z
Factor it out to get an anti-Hughes group of order 5^102
generated by a, b and c; and c^5 = NextQ.102
Z, its centre, has order 5^4
Now build a complement for c^5 in Z
Factor it out to get an anti-Hughes group of order 5^99
generated by a, b and c; and c^5 = NextQ.99
The centre is generated by CurrentQ.99 and has order 5^1
So this method reduces to an anti-Hughes group with order 5^99
which is as far as we can reduce the group (by this method!)
Total time: 128.312 seconds, Total memory usage: 632.31MB