Let $p$ be prime and let $T^p$ be the $p$-torus and $\mathbb{Z}/p$ the cyclic group of order $p$ generated by $(12\ldots p)$. Consider the semidirect product $T^p\rtimes\mathbb{Z}/p$ with the natural action.

I would like to know if the representation ring of this semidirect product is known. Alternatively, what is known about the cohomology of the classifying space $H^*(B(T^p\rtimes\mathbb{Z}/p);G)$ for $G$ either $\mathbb{Q}$ or $\mathbb{Z}$?