[GAP Forum] Automorphism Group as Permutation group on Conj.Classes

[Laurent Bartholdi]

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
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