function from A5 to A6 
Possible Duplicate:
Homomorphism between $A_5$ and $A_6$ 

Why is it true that every element of the image of the function $f: A_5\longrightarrow A_6$ (alternating groups) defined by $f(x)=(123)(456) x (654)(321)$ does not leave any element of $\{1,2,3,4,5,6\}$ fixed (except the identity)?

Whilst actually false, it is false because it leaves the $4$th element of the permutation fixed; like the function $f: x \to x$ leaves the $6$th element of the permutation fixed. (Dion didn't see that, he is using the geometrical proof)
I think in this problem, you have to use the geometrical proof, unless you find the permutation which $(123)$ will return yourself, which I've used Mathematica to determine.
