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I need help on question 1 I am preparing for my test:

1) Find a homomorphism $\alpha: A_4 \to\mathbb Z_6$ such that $\ker (\alpha) = K$ where $K$ is the normal subgroup $K= \{(1), (12)(34), (13)(24), (14)(23)\}$.

I am so confused on this I know the order of $A_4$ is $12$ and I listed all of them down and then found their orders but I am confused in how to obtain the answer.

2 Answers 2