Let $f$ be a homomorphism from $G$ to $G'$.
1) If order of a subgroup of $H$ of $G$ is $n$, then order of $f(H)$ divides $n$?
2) If the order of Kernel $f$ = $n$, then $f$ is a $n\times 1$ mapping from $G$ onto $f(G)$.
Please suggest how to proceed. Any feedback would be appreciated.