Prove A_4 Semidirect Product: Describe Homomorphism

[mathusers]

heres my final one. thnx.

Show that $A_4$, the group of even permutations on 4 letters, is a semidirect product:
$A_4 \cong (C_2 \times C_2) \rtimes_{\varphi} C_3$


and describe explicitly the associated homomorphism:
$\varphi : C_3 \rightarrow Aut(C_2 \times C_2)$

thnx for help on the previous posts.
any help here and ill attempt the rest myself

kind regards
x

 

[morphism]

Have you tried thinking about what A_4 looks like? It's not a very complicated group.