Let $G$ be a finite group and denote the centre of $G$ by $Z(G)$. Prove that if the quotient group $G / Z(G)$ is cyclic then $G$ is abelian. Does there exist a group $H$ such that (i) $|H / Z(H)|=7$ ? (ii) $|H| Z(H) \mid=6$ ?

Justify your answers.