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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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