1) Descibe explicitly all homomorphisms

h: C_6 ---> Aut(C_12)

C_6 ={1,x,....,x^5} x^6 = 1

We know that Aut(C_12) = {q_1,q_5,q_7,q_11} =~ C_2*C_2

where * = "cross" is the direct product

Then, h: C_6 ---> C_2*C_2

So, I found that the possibilities for h(x) are:

h_1(x) = 1

h_2(x) = q_5

h_3(x) = q_7

h_4(x) = q_11

Is that the right answer ? If wrong, please correct it

2)Describe explicitly all homomorphisms

h: C_5 ---> Aut(C_11)

Since 11 is prime number, so Aut(C_11) =~ C_10

I worked out that there are 5 homomorphism for C_5 ---> Aut(C_11). Is that true?

3)This question I dont know how to do it.

Show that Aut(C_2*C_2) =~ D_6 ( from cyclic group to dihedral group)

Thank you in advanced for your time