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 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 but a different reference to help me compare the possible approaches to the problem would be of great help!