What are some strategies for classifying p-groups?

[jgens]

I am working on classifying all groups of order less than or equal to 100. For most orders, this is fairly straightforward, since we can just utilize Cauchy's Theorem/Sylow's Theorems to show that the group can be expressed as a semi-direct product and then find the desired automorphism.

However, for p-groups the same procedure doesn't really work. In particular, I need to tackle the following two cases:

• Classify all groups of order p⁴ where p is a prime.
• Classify all groups of order 2^k where 5 ≤ k ≤ 6.

If anyone has any sources on these problems or knows how to tackle one them, the help is appreciated.

Thanks.

 

[fresh_42]

This becomes complicated fast. The reason is, that we have several identical copies which allows bigger automorphisms groups. Here is an example for $n=2^5$
https://groupprops.subwiki.org/wiki/Groups_of_order_32