[GAP Forum] a query

[Alexander Hulpke]

Dear GAP Forum,

On Dec 5, 2005, at 9:47 PM, Niranjan Balachandran wrote:

> hi,
>   i am interested in obtaining a (partial) lattice of subgroups of the
> symmetric group including all subgroups of size upto some small order.

(he specified in a private email that he is interested in small  
orders (e.g. 144) and small degrees)

For a nonsolvable group (there are better methods for solvable  
groups) such as Sn of small size, one can run the cyclic extension  
subgroup lattice program with a size limit (The the manual for more  
details):

g:=SymmetricGroup(10);;
  l:=LatticeByCyclicExtension(g,i->Size(i)<=100);
List(ConjugacyClassesSubgroups(l),Representative);

If the degree or subgroup order get larger this will fail for lack of  
memory. In this case one could use more theory and construct  
subgroups as subdirect products of transitive groups, using the  
transitive groups library.

I also would expect that in fact you are not interested in all  
subgroups up to the size, but only a subset. If you can specify these  
groups (in terms of order, composition factors, permutation action  
&c.) further, this might give substantial speedups.

All the best,

     Alexander Hulpke