# Online reference about semi-direct products in finite group theory?

The title says it all: Do you know a comprehensive (preferably online) reference about semi-direct products in (finite) group theory?

I would like to know much more about semi-direct products in the context of the classification of finite groups (of small order).

• What do you want to know? – Qiaochu Yuan Jan 15 '18 at 7:13
• I want to know, for example, given groups $H$ and $N$ and a homomorphism $\psi: H \to \text{Aut}(N)$ how to calculate a presentation for $N \rtimes_\psi H$, or what is the center of $N \rtimes_\psi H$? And more such stuff. – Tortoise Jan 15 '18 at 8:10
• A presentation is given by a presentation of $N$, concatenated with a presentation of $H$, and the additional relations $hnh^{-1} = \varphi(h)(n)$ for all $h, n \in H, N$. I don't think the center has a simple description (see math.stackexchange.com/questions/243327/… for some discussion). Mostly I think you should try to work out what you want to know as exercises. – Qiaochu Yuan Jan 15 '18 at 9:56