1) Describe explicitly all homomorphisms h: C_6 maps to Aut(C_12)

Firstly, I have to find what group Aut(C_12) is isomorphic to, and then find the order of that group. Is this the right track?

If it is, then I don't know how to do after this.

How do you find the homomorphism?

2) Find a subgroup H of sigma_8 ( permutation of {1,2,.......,8} ) such that H =~ Q8 ( H is isomorphic to the quanterion group of 8)

What should I do for this question?

Thanks alot to all your help.