Exercise
Let G be a group and C : G -> Sym(G) the conjugation representation. The image of C in Sym(G) is isomorphic to G/N for some normal subgroup N of G. Which of the following candidates is the right N?
{e}
Z(G), the center of G
G
No.
If G is commutative then C is trivial, so this cannot be correct in general.
Yes.
No. This would mean that conjugation is always trivial.
Right.