Solution
= Solution
Such a group does exist. Take $H=S_3$. Its center is trivial, so
$$
H/Z(H)\cong S_3
$$
has order six. Therefore
$$
\boxed{H=S_3\text{ is an example}.}
$$
= Solution
Such a group does exist. Take $H=S_3$. Its center is trivial, so
$$
H/Z(H)\cong S_3
$$
has order six. Therefore
$$
\boxed{H=S_3\text{ is an example}.}
$$