[GAP Forum] Computing Subgroups of L3(4):2

[Joe Bohanon]

I'm having some trouble with ConjugacyClassesSubgroups on the maximal
subgroup L3(4):2_1 of HS.  I'm trying to use the ideas in a paper by
Pfeiffer to find all classes of subgroups of HS, by examining the classes of
subgroups of its maximal subgroups and fusing them in HS.  It might have
been done before, but I couldn't find it.

With L3(4):2_1, I've hit a roadblock.  I'm using the degree 100 permutation
representation and the GAP inline program from the ATLAS to get the
generators of this subgroup.  I'd use the ATLAS to find the maximal
subgroups of L3(4):2_1 and do the same sort of thing, but the online version
doesn't have that information.

GAP had no problem computing the classes of subgroups of the two U3(5):2
maximal classes, but when I set InfoLattice to 2, I can see that it stalls
immediately after it computes the zuppos.  It comes upon a "Recursion Depth
Trap" error if I try it from scratch and when I set the recursion depth to
0, I ended up stopping it after an hour or so of nothing.  What I find odd
is that it only takes 5 seconds to find the subgroup of L3(4).

If anyone can help me out with this, I'd be very grateful.  I suppose I
probably don't really need all of the conjugacy classes, but frankly I'm
still curious to know why it stalls so bad on a group just twice as big as
one that goes fast.

My next step will be to go line through line in the source code to find the
exact spot that's causing this to take so long.

Thanks
Joe