# Element structure of special linear group:SL(2,7)

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## Contents |

This article gives specific information, namely, element structure, about a particular group, namely: special linear group:SL(2,7).

View element structure of particular groups | View other specific information about special linear group:SL(2,7)

This article gives detailed information about the element structure of special linear group:SL(2,7), which is a group of order 336.

See also element structure of special linear group of degree two.

## Conjugacy class structure

Compare with element structure of special linear group of degree two over a finite field#Conjugacy class structure.

In the table below, we consider the group as . The information is stated for generic odd and then computed numerically for .

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 | 24 | 4 | 4 | 96 | [SHOW MORE] | ||

Diagonalizable over , i.e., field:F49, not over , i.e., field:F7. Must necessarily have no repeated eigenvalues. | For : , , | For : , , | For : , , | 42 | 3 | 126 | PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
| |||

Diagonalizable over , i.e., field:F7 with distinct diagonal entries |
For : , | For : , | For : , | 56 | 2 | 112 | [SHOW MORE] | |||

Total | NA | NA | NA | NA | NA | 11 | 336 | NA |