Math Help - homomorphism

1. homomorphism

Find all homomorphisms between Z_2 x Z_2 ->S_3. S_3 isthe symmetric group on 3 symbols.

2. Originally Posted by Chandru1
Find all homomorphisms between Z_2 x Z_2 ->S_3. S_3 isthe symmetric group on 3 symbols.

Every such homom. is uniquely and completely determined by the images of the generators of $\mathbb{Z}_2\times\mathbb{Z}_2$ ...and where to can an order 2 generator be mapped in $S_3$ ?

Tonio