Changes

Jump to: navigation, search
Particular cases
{| class="sortable" border="1"
! <math>q</math> (field size) !! <math>p</math> (underlying prime, field characteristic) !! Case for <mah>q</math> !! Group <math>PGL(2,q)</math> !! Order of the group (<math>= q^3 - q</math>) !! Degrees of irreducible representations (ascending order) !! Number of irreducible representations (<math>= q + 1</math> if <math>q</math> even, <math>q + 2</math> if <math>q</math> odd) !! Linear representation theory page
|-
| 2 || 2 || even || [[symmetric group:S3]] ||6 || 1,1,2 || 3 || [[linear representation theory of symmetric group:S3]]
|-
| 3 || 3 || odd || [[symmetric group:S4]] ||24 || 1,1,2,3,3 || 5 || [[linear representation theory of symmetric group:S4]]
|-
| 4 || 2 || even || [[alternating group:A5]] ||60 || 1,3,3,4,5 || 5 || [[linear representation theory of alternating group:A5]]
|-
| 5 || 5 || odd || [[symmetric group:S5]] ||120 || 1,1,4,4,5,5,6 || 7 || [[linear representation theory of symmetric group:S5]]
|-
| 7 || 7 || odd || [[projective general linear group:PGL(2,7)]] ||336 || 1,1,6,6,6,7,7,8,8 ||9 || [[linear representation theory of projective general linear group:PGL(2,7)]]
|-
| 8 || 2 || even || [[projective special linear group:PSL(2,8)]] || 504 || 1,7,7,7,7,8,9,9,9 || 9 || [[linear representation theory of projective special linear group:SL(2,8)]]
|-
| 9 || 3 || odd ||[[projective general linear group:PGL(2,9)]] || 720 || 1,1,8,8,8,8,9,9,10,10,10 || 11 || [[linear representation theory of projective general linear group:PGL(2,9)]]
|}
Bureaucrats, emailconfirmed, Administrators
38,756
edits

Navigation menu