There is no group whose quotient by the center is isomorphic to the quaternion group

Question

I have to prove that there is no group $G$ such that $G/Z(G)$ is isomorphic to $Q_8$.

Anytone can give me an idea to begin? thanks

Answer 1

Hint: Let $i,j$ be generators of $Q_8$. Then $-1$ belongs to $\langle x\rangle$ for $x\in \{i,j\} $.