Prove that the dihedral group of order 4 is isomorphic to V, the four group.

My Proof:

V = {(1), (12)(34), (13)(24), (14)(23}

D4 = {e, o, t, ot} where o is rotations and t is reflections

So,

f(e) = (1)

f(o) = (12)(34)

f(t) = (13)(24)

f(ot) = (14)(23)

This is clearly a bijection by inspection. We must now show f is a homomorphism

I don't know where to go from here. Please explain and let me know of anything i've done wrong so far above. Thanks