I need to construct all homomorphisms from Klein-4 group $K_4$ to Symmetric group $S_3$. I could construct 10 homomorphisms listed below:
Are there any more homomorphisms possible to construct?
Many thanks in advance!
2026-03-28 04:34:23.1774672463
All homomorphisms from $K_4$ to $S_3$
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Hint: The Klein-$4$-group $V_4$ is generated by two elements. Thus every homomorphism $V_4 \rightarrow S_3$ is determined by the images of the two generators. How many choices for these images do you have?