Linear representation theory of unitriangular matrix group of degree five over a finite field

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This article gives specific information, namely, linear representation theory, about a family of groups, namely: unitriangular matrix group of degree five. This article restricts attention to the case where the underlying ring is a finite field.
View linear representation theory of group families | View other specific information about unitriangular matrix group of degree five | View other specific information about group families for rings of the type finite field

This article describes the linear representation theory of the unitriangular matrix group of degree five over a finite field of size q, where q is a prime power p^r with underlying prime p. p is the characteristic of the field.

Related information

Summary

Item Value
number of conjugacy classes (equals number of irreducible representations over a splitting field) 5q^4 - 5q^2 + 1. See number of irreducible representations equals number of conjugacy classes, element structure of unitriangular matrix group of degree four over a finite field
degrees of irreducible representations 1 (occurs q^4 times)
q (occurs 2q^4 - q^3 - q^2 = q^2(q - 1)(2q + 1) times)
q^2 (occurs 2q^4 - q^3 - 2q^2 + q = q(q - 1)(q + 1)(2q - 1) times)
q^3 (occurs 2q^3 - 3q^2 + q = q(q-1)(2q - 1) times)
q^4 (occurs q^2 - 2q + 1 = (q - 1)^2 times)
sum of squares of degrees of irreducible representations q^{10} (equals order of the group)
see sum of squares of degrees of irreducible representations equals order of group
lcm of degrees of irreducible representations q^4