Let G be a finite group. We know it can be written as a subgroup of S_n. On the other hand, people sometimes say Rep(G) --- the category of all finite dimensional representations, are more interesting to study.

So my question is, if we pass to Rep(G), how can we relate Rep(G) and Rep(S_n)? I can imagine there will be some functor given by restrictions. But are there other way to connect them?