Dear GAP-forum, dear Giulio Peruginelli,
I have a finite group G and I want to compute a representation of
Aut(G)
as a permutation group on the set of the conjugacy classes of G.
So I wrote down these lines in Gap 3
AutG:=AutomorphismGroup(G);
C:=ConjugacyClasses(G);
D:=[];
for k in [1..Length(C)] do
D[k]:=Representative(C[k]);
od;
AutG1:=Operation(AutG,D);
This ``action'' on the representatives of classes is not well defined
-- the image of a representative is not necessarily a representative.
Instead you will have to act on the classes themselves. For this you
will have to define your own action. The following is GAP4 code for it:
(In GAP3 you would need `cl.group' instead of `ActingDomain(cl)' and
`Operation' instead of `Action' I believe.)
OnClasses:=function(cl,g) # function to describe the action
return ConjugacyClass(ActingDomain(cl),Representative(cl)^g);
end;
AutG:=AutomorphismGroup(G);
C:=ConjugacyClasses(G);
Action(AutG,C,OnClasses);
If you need the connection to the original group you might prefer:
ActionHomomorphism(AutG,C,OnClasses,"surjective");
instead of `Action'.
Best,
Alexander Hulpke
-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: [EMAIL PROTECTED], Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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