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

## Contents

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 $q$ the size of the field and by $p$ the prime number that is the characteristic of the field. $q$ is a prime power with underlying prime $p$.

## Summary

Item Value
order of the group $(q^4 - 1)(q^4 - q)(q^4 - q^2)(q^4 - q^3) = q^6(q^4 - 1)(q^3 - 1)(q^2 - 1)(q - 1)$. In factored form over the rationals, this is $q^6(q-1)^4(q+1)^2(q^2 + 1)(q^2 + q + 1)$
number of conjugacy classes $q^4 - q = q(q^3 - 1) = q(q - 1)(q^2 + q + 1)$
See number of conjugacy classes in general linear group of fixed degree over a finite field is polynomial function of field size