Let $\phi$ be a homomorphism from a group $G$ onto a group $G'$. Prove that if $G$ is finite, then $G'$ is also ﬁnite and $|G'|$ divides $|G|$.
I know i should be using the Fundamental Homomorphism Theorem.
I also know that the Fundamental Homomorphism Theorem relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism. Can you help me start this proof off?