[GAP Forum] ConjugacyClassesSubgroups

[Max Horn]

Dear Tim,

> On 2. Dec 2020, at 23:47, tkohl at math.bu.edu wrote:
> 
> 
> Is there a way to call ConjugacyClassesSubgroups with
> a fixed size for the subgroups desired, so as to avoid
> having it spend time computing those of other sizes?
> 
> Right now I'm doing something like this:
> 
> Filtered(ConjugacyClassesSubgroups(G),x->Size(Representative(x))=n);
> 
> 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/...)?


Cheers
Max