Hi!

First, I am a relatively new user of GAP, as well as a novice on
group theory. My question is...

I am trying to explicitly find all sub-direct products of the direct
product group SxGxS, where S and G are both 2-groups, which have the
property that the subgroup of elements of the form {(e,g,s)} (e is
identity of S, g is in G and s is in S) have a particular order (such as 4).

The size of S is typically 8,16 or 32 while G is 32, 64 or 128.

My questions are...

1) In general, does anyone have any guidelines as to the most efficient
presentations of these groups for calculation in GAP?

2) In specific, does anyone have ideas for a good course of action for
this problem.

I have so far been trying to use the Ag presentations from the 2-groups
library for S and G then forming the DirectProduct. GAP seems to compute
with this presentation fairly fast, but clearly an attempt to, say, use
Lattice seems futile (the direct products are 2k-128K in size!).

Anyway, any input would be greatly appreciated, particularly as to whether
the representation from the 2-group library or a permutation rep would
be more efficient.

thanks...

-eric (ejr@ee.cornell.edu)