[GAP Forum] Finding certain subgroups from very large group

[Alexander Konovalov]

Dear Kher Sham Lim,

Thank you for your question. In fact, the very first hint is contained in the documentation of 'AllSubgroups' from the manual of the SONATA package:

  For  a  finite  group  G  AllSubgroups returns a list of all subgroups of G,
  intended  primarily  for  use  in  class  for small examples. This list will
  quickly  get  very  long  and  in  general  use of ConjugacyClassesSubgroups
  (39.19-3) is recommended

Further hints may be found in the GAP F.A.Q. at http://www.gap-system.org/Faq/faq.html#7.7 - for convenience, that text is also pasted below:

---------

7.7: How do I get the subgroups of my group?

Everything said for elements holds even more so for subgroups: You probably want only representatives of the conjugacy classes or even just of subgroups of a given size.

For groups of moderate size (up to 10^4/10^5, this depends a bit on the group structure) the commands LatticeSubgroups or ConjugacyClassesSubgroups will compute representatives of all subgroups up to conjugacy. If the group gets bigger, however, this will either run out of space or take too long to be feasible.

In this case it is likely that you are only interested in certain types of subgroups. Try to use the restricting conditions to reduce the calculation (for example p-subgroups can be found inside a Sylow subgroup). GAP commands that might come useful to obtain specific subgroups are for example NormalSubgroups,SylowSubgroup, HallSubgroup, or MaximalSubgroupClassReps.

----------

Hope this helps. There may be better suggestions, if more details would be known about the groups in question.

Best wishes,
Alexander



On 1 Feb 2013, at 11:33, Kher Sham Lim wrote:

> Dear GAP forum
> 
> I have a very large group to study, say G (it is an automorphism group of a small group). G has order of 10 million and I am interested in knowing whether a certain known group, say H is a subgroup in G. To find H is impossible in GAP, as GAP tries to calculate all the subgroups and this process exceeds my computer's memory. Is there another command or algorithm in GAP to compute subgroup of specific order only, or at least limit the subgroup order? I used SONATA to obtain the subgroups by the way. Thanks in advanced.
> 
> Sincerely
> 
> Kher Sham Lim
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum