# Linear representation theory of projective semilinear group of degree two over a finite field

## Contents

This article gives specific information, namely, linear representation theory, about a family of groups, namely: projective semilinear group of degree two.
View linear representation theory of group families | View other specific information about projective semilinear group of degree two

Item Value

## Particular cases $q$ (field size) $p$ (underlying prime, field characteristic) $r$ (size of Galois group) $P\Gamma L(2,q)$ Order of $P\Gamma L(2,q)$ (= $r(q^3 - q)$) number of irreducible representations (equals number of conjugacy classes degrees of irreducible representations linear representation theory page
2 2 1 symmetric group:S3 6 3 1,1,2 linear representation theory of symmetric group:S3
3 3 1 symmetric group:S4 24 5 1,1,2,3,3 linear representation theory of symmetric group:S4
4 2 2 symmetric group:S5 120 7 1,1,4,4,5,5,6 linear representation theory of symmetric group:S5
5 5 1 symmetric group:S5 120 7 1,1,4,4,5,5,6 linear representation theory of symmetric group:S5
7 7 1 projective general linear group:PGL(2,7) 336 9 1,1,6,6,6,7,7,8,8 linear representation theory of projective general linear group:PGL(2,7)
8 2 3 Ree group:Ree(3) 1512 11 1,1,1,7,7,7,8,8,8,21,27 linear representation theory of Ree group:Ree(3)
9 3 2 automorphism group of alternating group:A6 1440 13 1,1,1,1,9,9,9,9,10,10,16,16,20 linear representation theory of automorphism group of alternating group:A6
11 11 1 projective general linear group:PGL(2,11) 1320 13 1,1,10,10,10,10,10,11,11,12,12,12,12 linear representation theory of projective general linear group:PGL(2,11)