Automorphisms of non-abelian groups of order $ p^3$ There are two non-abelian groups of order $p^3$, namely, semi-direct product of $\mathbb Z /p \mathbb Z \times \mathbb Z /p \mathbb Z$ by $\mathbb Z /p \mathbb Z$ and semi-direct product of $\mathbb Z /p^2 \mathbb Z$ by $\mathbb Z /p \mathbb Z$. What are the automorphism groups of these groups?
 A: For the latter group, the answer is Bidwell, J. N. S.; Curran, M. J., The automorphism group of a split metacyclic $p$-group, Arch. Math. 87, No. 6, 488–497 (2006). Zbl 1116.20016.
A: The automorphism groups of all p-groups of order p^3 can be found at http://www.math.kth.se/~boij/kandexjobbVT11/Material/pgroups.pdf
A: There is a clear and more specific answer (with reference moreover!) here, despite the different question: https://math.stackexchange.com/a/18496/84625 
In short $\operatorname{Aut}\left(\left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \mathbb{Z}_p) \right) \cong  \operatorname{AGL}(2,p)$ while $\operatorname{Aut}\left(\mathbb{Z}_{p^2} \rtimes \mathbb{Z}_p \right) \cong \left(\mathbb{Z}_p \times \mathbb{Z}_p\right) \rtimes \operatorname{AGL}(1,p)$
where $\operatorname{AGL}(n,p)$ is the General Affine Group .
A: The former group can be seen as the group of unitriangular $3 \times 3$-matrices over the field with $p$ elements:
$$G = \left\{ \begin{pmatrix} 1 & * & * \\ 0 & 1 & * \\ 0 & 0 & 1 \end{pmatrix} \right\} \leq SL(3,p)$$
The automorphism groups of such groups have been studied (in a much larger generality); see for instance the paper "The automorphism group of the group of unitriangular matrices over a field" by Ayan Mahalanobis (http://arxiv.org/abs/1012.5534v1).
