Element structure of special linear group:SL(2,5)
From Groupprops
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
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 | Number of such conjugacy classes | Total number of elements | Semisimple? | Diagonalizable over ![]() |
Splits in ![]() ![]() |
Representative matrices (one per conjugacy class) |
---|---|---|---|---|---|---|---|---|---|---|
Scalar | ![]() ![]() |
![]() ![]() |
![]() ![]() |
1 | 2 | 2 | Yes | Yes | No | ![]() ![]() |
Not diagonal, Jordan block of size two | ![]() ![]() |
![]() ![]() |
![]() ![]() |
12 | 4 | 48 | No | No | Yes | ![]() ![]() ![]() ![]() |
Diagonalizable over field:F25, not over field:F5. Must necessarily have no repeated eigenvalues. | pair of square roots of ![]() ![]() |
![]() ![]() |
![]() ![]() |
20 | 2 | 40 | Yes | No | No | ![]() ![]() |
Diagonalizable over field:F5 with distinct diagonal entries | ![]() |
![]() |
![]() |
30 | 1 | 30 | Yes | Yes | No | ![]() |
Total | NA | NA | NA | NA | 9 | 120 | 72 | 32 | 48 | NA |