[GAP Forum] ConjugacyClassesSubgroups

[tkohl at math.bu.edu]

Hi

> > which seems rather inefficient.
> 
> Building up the subgroups of size n in general requires first constructing all
> smaller subgroup (resp. their classes). This can be done with LatticeByCyclicExtension:
> 
> LatticeByCyclicExtension(G, G -> Size(G) <= n);
> 
> However, this is not necessarily faster than ConjugacyClassesSubgroups. E.g. for A_10 as input, on my laptop ConjugacyClassesSubgroups(G) takes 5 seconds, while
>   LatticeByCyclicExtension(G, G -> Size(G) <= 10);
> requires almost 19 seconds.
> 
> What type and size of group is G, and how big is n? Do you have further restrictions about the subgroups you need? (E.g. perhaps they must be solvable/perfect/simple/...)?

Thanks for the information.

The groups in question are somewhat large, but the subgroups I'm looking for are comparatively
small. Basically I have H normal in N with quotient T and I am trying to find sections of
H -> N -> T inside N if there are any. Perhaps I could use the fact that the subgroups 
I'm looking for would have to constitute a transversal of H in N, but I'm not sure if 
that helps or not.


	-T