# Element structure of general linear group of degree four over a finite field

From Groupprops

This article gives specific information, namely, element structure, about a family of groups, namely: general linear group of degree four.

View element structure of group families | View other specific information about general linear group of degree four

This article discusses the element structure of the general linear group of degree four over a finite field.

We denote by the size of the field and by the prime number that is the characteristic of the field. is a prime power with underlying prime .

## Summary

Item | Value |
---|---|

order of the group | . In factored form over the rationals, this is |

number of conjugacy classes | See number of conjugacy classes in general linear group of fixed degree over a finite field is polynomial function of field size |

## Related information

### Other linear groups of degree four

- Element structure of special linear group of degree four over a finite field
- Element structure of projective general linear group of degree four over a finite field
- Element structure of projective special linear group of degree four over a finite field

## Conjugacy class structure

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