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If the user is working with enumerated sets of pc-groups
that are all subgroups of a common over-group G, then the following
optimization is strongly recommended. Define the set to have
the universe PowerGroup(G). For any subgroup H of G, we
can find a canonical form for the generators of H. This allows us
to have a very good hashing function for the subgroups.
The following example illustrates the optimization.
> G := ExtraSpecialGroup( GrpPC, 3, 3 );
> P := PowerGroup(G);
> time s1 := { P | sub< G | Random(G), Random(G) > : x in { 1..500 } };
Time: 1.140
> time s2 := { Parent(G) | sub< G | Random(G), Random(G) > : x in { 1..500 } };
Time: 9.769
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