Dear Forum, On Mar 5, 2017, at 11:24 AM, Benjamin Sambale <benjamin.samb...@gmail.com<mailto:benjamin.samb...@gmail.com>> wrote: the class function manual says: "The power of a class function by an element that normalizes the underlying group or by a Galois automorphism is the conjugate class function.”
G:=Group((1,2),(3,4)); a:=Elements(AutomorphismGroup(G))[2]; Irr(G)[1]^a; Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 3rd choice method found for `^' on 2 arguments Well, `a` is not an element (of a larger group) that normalizes the underlying group (in fact this automorphism cannot be realized by conjugation), nor a Galois automorphism. (The identity *is* a Galois automorphism, albeit a boring one.) If you take the regular representation, you can take equivalent conjugating elements of S_4, and it works as expected. gap> G:=Group((1,2)(3,4),(1,3)(2,4));; gap> c:=Irr(G)[1]; Character( CharacterTable( Group([ (1,2)(3,4), (1,3)(2,4) ]) ), [ 1, 1, 1, 1 ] ) gap> a:=Elements(AutomorphismGroup(G));;Length(a); 6 gap> List(a,IsConjugatorAutomorphism); [ true, true, true, true, true, true ] gap> a:=List(a,ConjugatorOfConjugatorIsomorphism); [ (), (3,4), (2,3), (2,3,4), (2,4,3), (2,4) ] gap> List(a,x->c^x); [ Character( CharacterTable( Group([ (1,2)(3,4), (1,3)(2,4) ]) ), [ 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (1,2)(3,4), (1,3) (2,4) ]) ), [ 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (1,2) (3,4), (1,3)(2,4) ]) ), [ 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (1,2)(3,4), (1,3)(2,4) ]) ), [ 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (1,2)(3,4), (1,3) (2,4) ]) ), [ 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (1,2) (3,4), (1,3)(2,4) ]) ), [ 1, 1, 1, 1 ] ) ] Regards, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@colostate.edu<mailto:hul...@colostate.edu>, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
