# Changes

## Element structure of special linear group:SL(2,5)

, 07:06, 13 August 2016
Interpretation as double cover of alternating group
{| class="sortable" border="1"
! Partition !! Partition in grouped form !! Does the partition have at least one even part? !! Does the partition have a repeated part? !! Conclusion: does the conjugacy class split from <matH>S_n[/itex] to $A_n$ in 2? !! Conclusion: does the fiber in $2 \cdot A_n$ over a conjugacy class in $A_n$ split in 2? !! Total number of conjugacy classes in <matH>2 \cdot A_n[/itex] corresponding to this partition (4 if Yes to both preceding columns, 2 if Yes to one and No to other, 1 if No to both) !! Size of each conjugacy class !! Size formula (we take the size formula in <matH>S_n[/itex], multiply by 2, and divide by the number (1,2, or 4) two columns preceding ) !! Total number of elements (= twice the size of the $S_n$-conjugacy class) !! Element orders !! Formula for element orders
|-
| 1 + 1 + 1 + 1 + 1 || 1 (5 times) || No || Yes || No || Yes || 2 || 1 || $\frac{2}{2} \frac{5!}{(1)^5(5!)}$ || 2 || 1 (1 class), 2 (1 class) || $\operatorname{lcm} \{ 1 \}$ (1 class)<br>$2\operatorname{lcm} \{ 1 \}$ (1 class)