[GAP Forum] Error using ConjugacyClassesSubgroups on S14

[Alexander Hulpke]

Dear Forum, Dear Jason Ives,

> On Jul 27, 2015, at 5:58 PM, Jason Ives <jasonives1993 at hotmail.com> wrote:
> 
> GAP, Version 4.7.8 of 09-Jun-2015 (free software, GPL)
> 
> gap> ConjugacyClassesSubgroups(SymmetricGroup(14));
> 
> Error, no method found! For debugging hints type ?Recovery from NoMethodFound
> Error, no 1st choice method found for `LengthsTom' on 1 arguments called from
> LengthsTom( recog[2] ) called from
> 
> It works for n<14, but seems to error for 14 and above. Is this a known issue?

Thank you for reporting this issue. I will fix it for future releases.

The problem is that GAP does not know the table of marks for A14 (or larger groups) and thus cannot use table lookup. However this means that after fixing the bug the command will run into generic code and almost certainly run out of memory.
> 
> I realize the computation may take time and memory, but 75154 classes for 14 should be manageable, no?

The issue is not just storing the result, but computing the groups which will involve conjugates (and thus far more groups than the class representatives) and the fact that a generic algorithm will not perform optimally in every special situation — in this example I am doubtful about termination.
> 
> Or is there a better way to get a representative of every permutation group for a given degree?

Yes. First you might want to think whether you really need all classes, or only particular ones. Transitive groups have been classified for the degrees you are interested in, intransitive ones can be constructed as subdirect products (which is how this number 75154 was obtained by Holt).

I might still have copies of such lists — if you indeed need a full list of these groups for your research tell me what you are trying to do, and I will see whether I can find these lists.

Regards,

   Alexander Hulpke

-- Alexander Hulpke,  Department of Mathematics, Colorado State University, 
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, http://www.math.colostate.edu/~hulpke