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
_______________________________________________
Forum mailing list
[email protected]
http://mail.gap-system.org/mailman/listinfo/forum
