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## Main Question or Discussion Point

For any element [tex]x \in A_5[/tex], we have that [tex][A_5:C_{A_5}(x)]=\begin{cases}

[S_5:C_{S_5}(x)], & \text{condition 1} \\

\frac{1}{2}[S_5:C_{S_5}(x)], & \text{condition 2}

\end{cases}[/tex]

Basically I want to know what the conditions are.

Note that [tex]C[/tex] is the centralizer.

[S_5:C_{S_5}(x)], & \text{condition 1} \\

\frac{1}{2}[S_5:C_{S_5}(x)], & \text{condition 2}

\end{cases}[/tex]

Basically I want to know what the conditions are.

Note that [tex]C[/tex] is the centralizer.