For the purpose of classifying another algebraic structure which is parametrised by the choice of a group and of an automorphism I need the classification up to isomorphism of automorphism groups of p-groups of order $p^4$.


I duly searched the web for a while and all the group theory manuals I could lay my hands on but I didn't find anything, not a hint.
Could someone provide a reference?


I already posted the same question on maths stack exchange and [Professor Holt](https://mathoverflow.net/users/35840/derek-holt) guessed that there is no publication on the subject. I repost here to verify his guess thoroughly.


A good reference for the classification of groups of order $p^4$ would be useful too, since I found the following thesis [On p-groups of low power order](http://www.math.kth.se/~boij/kandexjobbVT11/Material/pgroups.pdf) but a different reference to help me compare the possible approaches to the problem would be of great help!



Classification of automorphism groups of groups of order $p^4$
There is a description of the automorphism groups of groups of order $p^4$ in the Thesis by [B. Girnat: "Klassifikation der Gruppen bis zur Ordnung $p^5$." Staatsexamensarbeit, TU Braunschweig, 2003](https://arxiv.org/abs/1806.07462), whose advisor was B. Eick.
The description is given in terms of the action on a set of generators of the respective group.
If I may add a personal note, I have been searching for this information for a long time, and I found it incredible that such a basic and old topic had no treatment whatsoever published in any form on the web. But I was assuming that anything interesting can be found in English (either written or translated into it). This assumption has been proven wrong, and I state this here as a warning for the newbies like me! 


