# Semi Direct Product

1. Feb 2, 2008

### mathusers

thnx for helping on the previous post.

heres the next one, as usual any hints on how to approach the question would be greatly appreciated. i will attempt the questions with the hints :)

(1)
describe explicitly all homomorphisms

$\varphi : C_4 \rightarrow Aut(C_5)$

(2)
For each such homomorphism $\varphi$ describe the semidirect product $C_5 \rtimes_{\varphi} C_4$ in terms of generators and relations.

(3) How many distinct isomorphism types of groups of the form $C_5 \rtimes_{\varphi} C_4$ are there?

2. Feb 3, 2008

### morphism

It will help to know what Aut(C_5) is. Hint: It's cyclic.