[GAP Forum] Re: All subgroups

[Alexander Hulpke]

Dear GAP-Forum,

A. Javed wrote:

> I am working on GAP. Pls tell me how to construct All Possible Subgroups of a
> FpGroup by using GAP Thanks

I suppose you don't really want all subgroups but that subgroups up to
conjugacy will be sufficient.

The general function for classes of subgroups is
`ConjugacyClassesSubgroups'.

However for FpGroups you are likely better off to first convert to an
isomorphic permutation group:

  hom:=IsomorphismPermGroup(g);
  p:=Image(hom);
  cl:=ConjugacyClassesSubgroups(p);;
  cl:=List(cl,i->PreImage(hom,Representative(i)));

gives a list of subgroups up to conjugacy.

Please note that the feasibility of the calculations depends very much on
the order of the FpGroup you use. I would expect problems if it is larger
than a few 10000s.

Best,

   Alexander Hulpke