Changes

Linear representation theory of projective general linear group of degree two over a finite field

, 19:23, 1 November 2011
Particular cases
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! [itex]q[/itex] (field size) !! [itex]p[/itex] (underlying prime, field characteristic) !! Case for <mah>q[/itex] !! Group [itex]PGL(2,q)[/itex] !! Order of the group ([itex]= q^3 - q[/itex]) !! Degrees of irreducible representations (ascending order) !! Number of irreducible representations ([itex]= q + 1[/itex] if [itex]q[/itex] even, [itex]q + 2[/itex] if [itex]q[/itex] 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)]]
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