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

Joe Bohanon jbohanon2 at gmail.com
Tue May 5 17:42:10 BST 2009

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.

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've thought about using the ideas from the paper "Constructing 
Permutation Representations for Large Matrix Groups", but before I 
embark on trying to encode their algorithm, I figured I'd ask here to 
see if anyone might just happen to have generators you could send me.


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