Holomorph of Cyclic $p$-groups

Question

Assume that $G$ is a cyclic $p$-group (or up to isomorphism more explicitly $\mathbb{Z}_{p^r}$). Do you know if there does exist any explicit way to describe the holomorph of the above group? Moreover, do you know if we can say something about the representations of these groups? (modular, non-modular)

Answer 1

My representation theory is almost nada.

But the holomorph is, ims, the canonical semi-direct product $G\rtimes\rm_\varphi {Aut}G $, with the action being left multiplication.

So we get $\mathbb Z_{p^r}\rtimes_\varphi\mathbb Z_{p^r-p^{r-1}} $, unless $p=2$.