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There are (at least) three ways to define a cyclic of order 12 in Sage:
sage: C12 = groups.permutation.Cyclic(12)
sage: G12 = AbelianGroup([12])
sage: H12 = AdditiveAbelianGroup([12])
Now evaluate C12.gens() (for example): how many generators does this group have? Any homomorphism is determined by where the generators go. So what are the possible endomorphisms (= homomorphisms from the group to itself) of this group? Can you figure out which of them are actually automorphisms?
