[GAP Forum] Symmetric bicharacters

[Dan Lanke]

Dear GAP Forum,

Let A be a finite abelian group. Let C^* denote the multiplicative group of non-zero complex numbers. Let Hom(A, C^*) denote the group of all homomorphisms from A to C^*. 

I would like to create the group of all isomorphisms f : A --> Hom(A,  C^*) that satisfy

(f(a))(b) = (f(b))(a), for all  a,b \in A.

Could you please point me in the right direction?

Many thanks,
Dan