Dear GAP Forum,
Joe Bohanon asked
> Does anyone know a good way to get a permrep for 3.McL.2 (the second
> largest subgroup of the Lyons group)? The ATLAS has a rep for 3.McL
> with about 66k moved points, so I'm guessing 3.McL.2 is probably not
> much bigger than that.
You can take the permutations stored in
http://www.math.rwth-aachen.de/~mfer/datagens/3McLd2G1-p66825bB0.m1
http://www.math.rwth-aachen.de/~mfer/datagens/3McLd2G1-p66825bB0.m2
> What I really need is a list of the classes of non-solvable subgroups of
> 3.McL.2. I could theoretically do this by creating a homomorphism to
> McL.2, then lifting non-solvable subgroups and testing if the "3" is
> complemented or not in the pre-images. I can easily create the
> homomorphism using GroupHomomorphismByImagesNC, but GAP stalls bad when
> trying to take pre-images.
I would start from the struture of the maximal subgroups of McL.2
(see the Atlas) and of 3.McL (see `Maxes( CharacterTable( "3.McL" ) )').
This should help to find the structures of the nonsolvable maximal subgroups
of 3.McL.2.
All the best,
Thomas Breuer
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