s

2

3

4

5

$G_{\alpha }$

${\text{A}}_5,S_5$

${\text{A}}_5\times S_5,\left({\text{A}}_5\times S_5\right):{\text{A}}_2,S_4\times S_5$

$\begin{array}{l}\text{ASL}\left(2,4\right),\text{AGL}\left(2,4\right),\\ \text{A}\Sigma \text{L}\left(2,4\right),\text{A}\Gamma \text{L}\left(2,4\right)\end{array}$

$Z_6:\Gamma \text{L}\left(2,4\right)$

$\left|G_{\alpha }\right|$

$60,120$

$720,1440,2880$

$960,2880,1920,5760$

23040