Prove that a group $G$ has a faithful irreducible representation over a field $F$ if and only if the centre of $G$ is cyclic

Question

An answer to this question would be greatly appreciated.

Let $G$ be a finite group and $F$ a field such that the order $\mid G\mid$ is coprime to the characteristic of $F$. Prove that $G$ has a faithful irreducible representation over $F$ if and only if the centre of $G$ is cyclic