# Element structure of general linear group over a finite field

From Groupprops

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

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

This article describes the element structure of the general linear group of finite degree over a finite field, i.e., a group of the form , also denoted , defined as the general linear group of degree over the (unique up to isomorphism) field of size .

This builds on conjugacy class size formula in general linear group over a finite field.

## Particular cases

### Particular cases by degree

Value of degree | Element structure of general linear group | order of group | degree as a polynomial in (= ) | number of conjugacy classes | degree as a polynomial in (= ) |
---|---|---|---|---|---|

1 | the general linear group is a cyclic group of size , given by the multiplicative group of -- see multiplicative group of a finite field is cyclic | 1 | 1 | ||

2 | element structure of general linear group of degree two over a finite field | 4 | 2 | ||

3 | element structure of general linear group of degree three over a finite field | 9 | 3 |