Do you understand how my hint gives you the result?...
Another approach would be to note that and so we can quotient out in both and .
I'm not sure where looking at the Kernel of the isomorphism would really get you. It made me conjour up the above paragraph, but I'm not sure what it would really do. However, in both of my solutions the actual group is irrelevent (as long as it is non-trivial), so I would suspect that there exists a solution that actually uses the group given...
Also, put the text [math-] and [/math-] (without the "-") around your maths to make it LeTeX-ey.
It’s not too hard to see that as follows.
Suppose is a homomorphism. Then since homomorphisms map identities to identities. Hence and so Similarly It follows that maps the four-element set to the two-element set So, what can you conclude here? Can be injective? Can it be an isomorphism?