Conditions for Index Size in A_5 and S_5 Centralizers

[epkid08]

For any element x \in A_5, we have that [A_5:C_{A_5}(x)]=\begin{cases}<br /> [S_5:C_{S_5}(x)], &amp; \text{condition 1} \\<br /> \frac{1}{2}[S_5:C_{S_5}(x)], &amp; \text{condition 2}<br /> \end{cases}

Basically I want to know what the conditions are.

Note that C is the centralizer.

 

[epkid08]

I'm just talking to myself here, but I think condition 1 is "x takes the form (abc)" and condition 2 is "x takes the form (abcde)."

Anybody want to verify?