- #1

mathusers

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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

[itex]\varphi : C_4 \rightarrow Aut(C_5)[/itex]

(2)

For each such homomorphism [itex]\varphi[/itex] describe the semidirect product [itex]C_5 \rtimes_{\varphi} C_4[/itex] in terms of generators and relations.

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