There is a clear and more specific answer (with reference moreover!) here, despite the different question: [http://math.stackexchange.com/a/18496/84625][1] 

In short $\mathsf{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong \mathsf{AGL}(2,p)$ while $\mathsf{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p) \right) \cong \mathbb{Z}_{p}^{*} \rtimes \mathsf{AGL}(1,p)$

where $\mathsf{AGL}(n,p)$ is the [Affine General Linear Group][2] over $ \mathbb{Z}_p^n$ and $\mathbb{Z}_p^{*}$ is the dual of $\mathbb{Z}_p$.


  [1]: http://math.stackexchange.com/a/18496/84625
  [2]: http://groupprops.subwiki.org/w/index.php?title=General_affine_group&oldid=40987