[GAP Forum] Permutation Representation of 3.McL.2

[Thomas Breuer]

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