[GAP Forum] Elementary abelian p-subgroups

[Jared Warner]

Dear GAP forum,

I'm interested in studying the Quillen Complex of a finite group G, which
is the lattice of elementary abelian p-subgroups of G.  Magma has a command
ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
do this with GAP (to avoid paying for Magma).

Specifically, given a finite group G I'd like to know:

1. The number of conjugacy classes of elementary abelian p-subgroups of a
certain rank

2. The number of subgroups in each such conjugacy class

3. A set of generators of a representative from each such conjugacy class

I'm aware of ConjugacyClassesSubgroups, but I'd like to my command return a
list of representatives of elementary abelian p-subgroups, not all
subgroups.

Also, I'd like to avoid working with ConjugacyClassesSubgroups if possible,
because it seems like a lot of wasted time and memory to compute the whole
subgroup lattice when I'm only interested in a small portion of it.

Thanks for any help!

Jared