Group homomorphisms between cyclic groups

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Describe al group homomorphisms \phi : C_4 --> C_6

The book I study from seems to pass over Group Homomorphisms very fast. So I decided to look at Artin's to help and it uses the same definition. So I think I am just not digesting something I should be. I know it's defined as \phi (a*b) = \phi (a) * \phi and that it maps the inverses to the inverses but I just have no idea how to apply these.
 
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I forgot a b in the definition of phi(a*b) = phi(a)*phi(b)
 
If you specify \phi(1), then what does this say about the value of \phi at the other elements in C_4? Also, a general fact about homomorphisms is that the order of \phi(g) must divide the order of g. Can you prove this? By the way, you can edit posts.
 

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