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

From Groupprops
Jump to: navigation, search
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

Related information

Other linear groups of degree four

Conjugacy class structure

PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]