  We consider the integer group determinants for groups that are semidirect
products of $\mathbb Z_p$ and $\mathbb Z_n$ with $p$ prime and $n\mid p-1$. We
give a complete description of the integer group determinants for the general
affine groups of degree one GA(1,5) and GA(1,7), and for $\mathbb Z_7\rtimes
\mathbb Z_3,$
  $\mathbb Z_{11}\rtimes \mathbb Z_5$ and $\mathbb Z_{13}\rtimes \mathbb Z_6,$
showing that the obvious divisibility and congruence conditions arising from
the form of the group determinant when $n=p-1$ or $\frac{1}{2}(p-1)$, can be
sufficient as well as necessary for these types of groups.
