# Smallest possible odd integer that can be the order of a non-Abelian group.

Smallest possible odd integer that can be the order of a non-Abelian group.

Attempt: A non abelian group means $Z(G) \subset G$ . Hence, it suffices to find the smallest odd integer $n$ such that $Z(G)$ is a proper sub group of $G$.

Unfortunately, I do not have a strategy in mind beyond this. How should I move ahead?

Hint: Recall that groups of order $pq$ and $p^2$ for $p,q$ primes with $p<q$ and $q\not\equiv 1 \pmod{p}$ are abelian. This rules out many "small" numbers.