Check Fulton and Harris this the natural representation on the exterior algebra (that is if is the representation came from).

You have yet to show any effort friend, come on.(2) Let G be a finite group, A is a normal subgroup of G; suppose that for all a in A' = (A \ {1}), A = C_g (a) and that G\A is abelian.

Show that G has exactly (|A|-1)/|G:A| irreducible characters of degree greater than or equal to 2, which have degree |G:A|