Find all the group morphisms from $C_3$ to $C_4$ I know that since the gcd of 3 and 4 is 1, there can only be one group morphism but I'm unsure of how to find it. Any help would be greatly appreciated!

Hint: If $\phi:C_{3}\to C_{4}$ is a group homomorphism, what will be the kernel and image of $\phi$? Especially, what is an order of $\ker(\phi)$? And also an order of $\mathrm{img}(\phi)$? Think about the Lagrange's theorem and the 1st isomorphism theorem. 
