- #1

jgens

Gold Member

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## Main Question or Discussion Point

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:

Thanks.

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 p
^{4}where p is a prime. - Classify all groups of order 2
^{k}where 5 ≤ k ≤ 6.

Thanks.