## help me to prove this..

(1) Let G=Sym(n) and $\theta \in Hom(C, G)$ where C is a cyclic group. Then $\gamma (Ker \theta)=Ker \theta$ , where $\gamma \in Aut(G)$.

(2) Can you explain , why this (1) breaks down for a non-cyclic abelian group? Pls give an example.