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"Let G be a cyclic group of order 7. Determine the number of homomorphisms from G to [itex]S_7[/itex]"

I know the definition of a cyclic group. It's a group generated by a single element. The order 7 means that [itex] g^7 = e [/itex] for g within G.

I understand that a homomorphism is defined by [itex] \Psi (ab) = \Psi(a)\Psi(b)[/itex] for a, b that exist in G. [itex] \Psi : G \rightarrow S_7 [/itex]

My main problem is, I can't put this all together and answer the question!

Any comments/suggestions would be appreciated

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# Homomorphism Q

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