[GAP Forum] Reducing memory usage for depth-first search

[Watson Ladd]

Dear all,
I'm interested in enumerating all extensions of S3 by a 2-group which
do not have elements of order greater than 6, of size up to 2^20.
(Yes, this is likely to be extremely difficult: I actually need to
look at extensions 1->N->G->S3->1, with N a 2 group of exponent 4)

I'm trying to use the Extensions function on PC group to compute
central extensions by C2 at each step, and for now just counting how
many there are, without isomorphism testing. Unfortunately this eats
up memory, even when carrying out a breadth first search.

So I have a number of questions:
1: Can I use Extensions(G,M) in a memory sparing-way, or will it have
to do a large construction of a list it pares down later?
2: How do I know what constructions are consuming memory? I'm only
constructing lists of groups: even long one shouldn't demand that much
memory, and the lists are short (hopefully).
3: Are there better algorithms than the naive one of taking central
extensions and filtering? I thought about taking all possible centers,
but C4 doesn't seem to be expressible as a module (I'm sure it is, but
I didn't figure it out).

Sincerely,
Watson Ladd