Element structure of special linear group:SL(2,5)
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This article gives specific information, namely, element structure, about a particular group, namely: special linear group:SL(2,5).
View element structure of particular groups | View other specific information about special linear group:SL(2,5)
This article gives detailed information about the element structure of special linear group:SL(2,5), which is a group of order 120.
See also element structure of special linear group of degree two.
Conjugacy class structure
Conjugacy classes
PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]Relationship with conjugacy class structure for an arbitrary special linear group of degree two
Further information: element structure of special linear group of degree two over a finite field
Nature of conjugacy class | Eigenvalue pairs of all conjugacy classes | Characteristic polynomials of all conjugacy classes | Minimal polynomials of all conjugacy classes | Size of conjugacy class (generic odd ![]() |
Size of conjugacy class (![]() |
Number of such conjugacy classes (generic odd ![]() |
Number of such conjugacy classes (![]() |
Total number of elements (generic odd ![]() |
Total number of elements (![]() |
Representative matrices (one per conjugacy class) |
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Scalar | ![]() ![]() |
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1 | 1 | 2 | 2 | 2 | 2 | ![]() ![]() |
Not diagonal, Jordan block of size two | ![]() ![]() |
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12 | 4 | 4 | ![]() |
48 | [SHOW MORE] |
Diagonalizable over field:F25, not over field:F5. Must necessarily have no repeated eigenvalues. | ![]() ![]() ![]() |
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20 | ![]() |
2 | ![]() |
40 | ![]() ![]() |
Diagonalizable over field:F5 with distinct diagonal entries | ![]() |
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30 | ![]() |
1 | ![]() |
30 | ![]() |
Total | NA | NA | NA | NA | NA | ![]() |
9 | ![]() |
120 | NA |