Dear Giulio,
I can't comment on GAP3, which I'm too young to have used :), but with
GAP4 the following gives you a permutation action:
gap> G:=SmallGroup(12,1);
<pc group of size 12 with 3 generators>
gap> AutG:=AutomorphismGroup(G);
<group of size 12 with 3 generators>
gap> C:=ConjugacyClasses(G);
[ <identity> of ...^G, f1^G, f2^G, f3^G, f1*f2^G, f2*f3^G ]
gap> Action(AutG,C,function(pnt,g)
return ConjugacyClass(G,Representative(pnt)^g); end);
Group([ (), (2,5), () ])
Action() takes a group, a set, and a function which describes the
action of an element of the group on an element of the set. The
function I put here takes a conjugacy class, picks a representative,
acts on it, and re-constructs a conjugacyclass.
Best, L
--
Laurent Bartholdi \ laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD \ Téléphone: +41 21-6935458
Station 8 \ Secrétaire: +41 21-6935471
CH-1015 Lausanne, Switzerland \ Fax: +41 21-6930339
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