Linear representation theory of projective special linear group:PSL(2,11)

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This article gives specific information, namely, linear representation theory, about a particular group, namely: projective special linear group:PSL(2,11).
View linear representation theory of particular groups | View other specific information about projective special linear group:PSL(2,11)

Summary

Item Value
degrees of irreducible representations over a splitting field (such as \overline{\mathbb{Q}} or \mathbb{C}) 1,5,5,10,10,11,12,12
in grouped form: 1 (1 time), 5 (2 times), 10 (2 times), 11 (1 time), 12 (2 times)
number: 8, sum of squares: 660, maximum: 12, quasirandom degree: 5, lcm: 660
number of irreducible representations (equals number of conjugacy classes) 8
As PSL(2,q), q = 11 (q odd): (q+ 5)/2 = (11 + 5)/2 = 8


Family contexts

Family name Parameter values General discussion of linear representation theory of family
projective special linear group of degree two PSL(2,q) over a finite field of size q q = 11, i.e., field:F11, so the group is PSL(2,11) linear representation theory of projective special linear group of degree two over a finite field

GAP implementation

Degrees of irreducible representations

These can be computed using the CharacterDegrees, GAP:CharacterTable, and PSL functions:

gap> CharacterDegrees(CharacterTable(PSL(2,11)));
[ [ 1, 1 ], [ 5, 2 ], [ 10, 2 ], [ 11, 1 ], [ 12, 2 ] ]

Character table

This can be computed using the Irr, CharacterTable, and PSL functions:

gap> Irr(CharacterTable(PSL(2,11)));
[ Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 5, 0, 0, E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,
      E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10, 1, -1, 1 ] ),
  Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 5, 0, 0, E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10,
      E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9, 1, -1, 1 ] ),
  Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 10, 0, 0, -1, -1, -2, 1, 1 ] ), Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 10, 0, 0, -1, -1, 2, 1, -1 ] ), Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 11, 1, 1, 0, 0, -1, -1, -1 ] ), Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 12, E(5)^2+E(5)^3, E(5)+E(5)^4, 1, 1, 0, 0, 0 ] ),
  Character( CharacterTable( Group(
    [ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]) ),
    [ 12, E(5)+E(5)^4, E(5)^2+E(5)^3, 1, 1, 0, 0, 0 ] ) ]