This is kinds of extension of Let G be a nonabelian group of order $p^3$, where $p$ is a prime number. Prove that the center of $G$ is of order $p$.
What i want to do is following
If $p$ is a prime number and $G$ is non-abelian group of order $p^3$, $G/Z(G) \cong Z_p \times Z_p$.
What i know is that $|Z(G)|=p$, and conclude the isomorphism to product of $Z_p$.
How to prove this?