I am trying to find the integers i for which SmallGroup(512,i) has derived
length 3 and commutator subgroup of order not exceeding 32, but it is
taking too long (more than an hour for something like 20.000 groups). I am
doing the following:

gap> l:=[];;
gap> for i in [1..NumberSmallGroups(512)] do
> G:=SmallGroup(512,i);
> D:=DerivedSubgroup(G);
> if Size(D)<33 and IsAbelian(D)=false then Add(l,i); fi;
> od;

What is the most efficient way to do what I want? Are groups of order 512
and derived length 3 somehow localized in the list of groups of this order
that GAP provides? (Or may be the more than 10 million groups of this
order are too many and I cannot hope to do this?) It seems to me that this
program is reasonably fast at the beginning but after a while it goes
slower and slower.

Many thanks,

Alexander Moreto

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