[GAP Forum] Creating all subgroups of SymmetricGroup

[Joe Bohanon]

All that you're looking for is stored in the table of marks library.

tom:=TableOfMarks("S9");
n:=Size(SubsTom(tom));
reps:=List([1..n],i->RepresentativeTom(tom,i));

This only gives one representative per conjugacy class.  I'd warn you that
there are 1,694,723 subgroups in all.

Also, FYI, the TOM library goes up to S12.

Joe

2009/11/4 Могильных Иван Юрьевич <ivmog84 at gmail.com>

> Hello, GAP forum!
> 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.
> But this record contains additional information and GAP is working too slow
> while trying to create it.
> Can I boost it somehow?
>
> Ivan
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