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?



Automorphisms of non-abelian groups of order $ p^3$
For the latter group, the answer is *Bidwell, J. N. S.; Curran, M. J.*, [**The automorphism group of a split metacyclic $p$-group**](https://doi.org/10.1007/s00013-006-1899-z), Arch. Math. 87, No. 6, 488–497 (2006). [Zbl 1116.20016](https://zbmath.org/?q=an:1116.20016).


