# 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 relative to ? | Representative matrices (one per conjugacy class) |
---|---|---|---|---|---|---|---|---|---|---|

Scalar | or | or | or | 1 | 2 | 2 | Yes | Yes | No | and |

Not diagonal, Jordan block of size two | or | or | or | 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 in field:F25, pair of square roots of in field:F25 | , | , | 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 |

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) |
---|---|---|---|---|---|---|---|---|---|---|

Scalar | or | or | or | 1 | 1 | 2 | 2 | 2 | 2 | and |

Not diagonal, Jordan block of size two | or | or | or | 12 | 4 | 4 | 48 | [SHOW MORE] | ||

Diagonalizable over field:F25, not over field:F5. Must necessarily have no repeated eigenvalues. | and , where is interpreted a an element of field:F25 that squares to 3 | , | , | 20 | 2 | 40 | , | |||

Diagonalizable over field:F5 with distinct diagonal entries |
30 | 1 | 30 | |||||||

Total | NA | NA | NA | NA | NA | 9 | 120 | NA |