Dear GAP forum,
Ivan Jurevitch asked:
Can I create the set(list/ record) of all subgroups (preferebly
nonisomorphic) of a Symmetric Group on 9 elements - Sym(9)?
There is a function IntermediateSubgroup(G,U) which creates all
subgroups
"between"G and U.
`IntermediateSubgroups' is intended for the case that U is nontrivial
and you don't want to get the full lattice. It likely is very
inefficient for getting all subgroups.
The command
Flat(List(ConjugacyClassesSubgroups(G),Elements));
creates a list of all subgroups. I doubt you would want to have this
list for S9 (which has 1694723 subgroups in 554 classes) -- you
probably will be happy with class representatives as obtained from
ConjugactyClassesSubgroups.
Also see questions 7.6 and 7.7 of the FAQ at
http://www.gap-system.org/Faq/Computing/computing.html
Best,
Alexander Hulpke
-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: [email protected], Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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