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

1 byte added, 07:06, 13 August 2016
Interpretation as double cover of alternating group
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! 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</math> to <math>A_n</math> in 2? !! Conclusion: does the fiber in <math>2 \cdot A_n</math> over a conjugacy class in <math>A_n</math> split in 2? !! Total number of conjugacy classes in <matH>2 \cdot A_n</math> 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</math>, multiply by 2, and divide by the number (1,2, or 4) two columns preceding ) !! Total number of elements (= twice the size of the <math>S_n</math>-conjugacy class) !! Element orders !! Formula for element orders
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| 1 + 1 + 1 + 1 + 1 || 1 (5 times) || No || Yes || No || Yes || 2 || 1 || <math>\frac{2}{2} \frac{5!}{(1)^5(5!)}</math> || 2 || 1 (1 class), 2 (1 class) || <math>\operatorname{lcm} \{ 1 \} </math> (1 class)<br><math>2\operatorname{lcm} \{ 1 \}</math> (1 class)
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