What is the character table for groups or order $pq^2$? The classification of order $pq^2$ groups has already been discussed in relation to Sylow theory.
For the Abelian groups, $\mathbb{Z}_p \oplus \mathbb{Z}_{q^2}$ and $\mathbb{Z}_p \oplus \mathbb{Z}_q \oplus \mathbb{Z}_q$, all the irreducible representations are 1-dimensional.
According to some group theory lecture notes I found online (bottom of page 8), there is only one other group when $q \not\equiv 1 (\mod p)$ and two when $q \equiv 1 (\mod p)$. I am asking for the character table in any or all of these cases.