Linear representation theory of McLaughlin group

This article gives specific information, namely, linear representation theory, about a particular group, namely: McLaughlin group.
View linear representation theory of particular groups | View other specific information about McLaughlin group

Summary

Item	Value
degrees of irreducible representations	1, 22, 231, 252, 770, 770, 896, 896, 1750, 3520, 3520, 4500, 4752, 5103, 5544, 8019, 8019, 8250, 8250, 9625, 9856, 9856, 10395, 10395 maximum: 10395, lcm: 898128000, number: 24, sum of squares: 898128000

GAP implementation

The character degrees can be computed using the CharacterDegrees and CharacterTable functions:

gap> CharacterDegrees(CharacterTable("McL"));
[ [ 1, 1 ], [ 22, 1 ], [ 231, 1 ], [ 252, 1 ], [ 770, 2 ], [ 896, 2 ], [ 1750, 1 ], [ 3520, 2 ], [ 4500, 1 ], 
[ 4752, 1 ], [ 5103, 1 ], [ 5544, 1 ], [ 8019, 2 ], [ 8250, 2 ], [ 9625, 1 ], [ 9856, 2 ], [ 10395, 2 ] ]

The full character table can be printed using the Irr and CharacterTable functions.[SHOW MORE]

gap> Irr(CharacterTable("McL"));
[ Character( CharacterTable( "McL" ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( "McL" ),
    [ 22, 6, -5, 4, 2, -3, 2, 3, 0, 1, 1, 0, 1, 1, 1, 0, 0, -1, -1, -1, 0, 0, -2, -2 ] ), Character( CharacterTable( "McL" ),
    [ 231, 7, 15, 6, -1, 6, 1, 7, -2, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 2, 2 ] ), Character( CharacterTable( "McL" ),
    [ 252, 28, 9, 9, 4, 2, 2, 1, 1, 0, 0, 0, 0, 0, -2, -1, -1, 1, 0, 0, -1, -1, 1, 1 ] ), Character( CharacterTable( "McL" ),
    [ 770, -14, -13, 5, -2, -5, 0, 7, 1, 0, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, -E(15)^7-E(15)^11-E(15)^13-E(15)^14, -E(15)-E(15)^2-E(15)^4-E(15)^8,
      -E(15)^7-E(15)^11-E(15)^13-E(15)^14, -E(15)-E(15)^2-E(15)^4-E(15)^8 ] ), Character( CharacterTable( "McL" ), [ 770, -14, -13, 5, -2, -5, 0, 7, 1, 0,
      0, 0, -1, -1, 1, 0, 0, 1, 0, 0, -E(15)-E(15)^2-E(15)^4-E(15)^8, -E(15)^7-E(15)^11-E(15)^13-E(15)^14, -E(15)-E(15)^2-E(15)^4-E(15)^8,
      -E(15)^7-E(15)^11-E(15)^13-E(15)^14 ] ), Character( CharacterTable( "McL" ), [ 896, 0, 32, -4, 0, -4, 1, 0, 0, 0, 0, 0, -1, -1, 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, 0, 0, 0, 2, 2, 0, 0 ] ), Character( CharacterTable( "McL" ),
    [ 896, 0, 32, -4, 0, -4, 1, 0, 0, 0, 0, 0, -1, -1, 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, 0, 0, 0, 2, 2,
      0, 0 ] ), Character( CharacterTable( "McL" ), [ 1750, 70, -5, 13, 2, 0, 0, -5, 1, 0, 0, 0, -2, -2, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 3520, 64, -44, 10, 0, -5, 0, 4, -2, -1, -1, 0, 1, 1, -1, 0, 0, 0, 1, 1, 1, 1, -1, -1 ] ),
  Character( CharacterTable( "McL" ), [ 3520, -64, -44, 10, 0, -5, 0, -4, 2, -1, -1, 0, 1, 1, 1, 0, 0, 0, -1, -1, 1, 1, 1, 1 ] ),
  Character( CharacterTable( "McL" ), [ 4500, 20, 45, -9, 4, 0, 0, 5, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, -1, -1, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 4752, -48, 54, 0, 0, 2, 2, -6, 0, -1, -1, 0, 0, 0, 2, 0, 0, 0, 1, 1, -1, -1, -1, -1 ] ),
  Character( CharacterTable( "McL" ), [ 5103, 63, 0, 0, 3, 3, -2, 0, 0, 0, 0, 1, 0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 5544, -56, 36, 9, 0, 19, -1, 4, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, -1, -1 ] ),
  Character( CharacterTable( "McL" ), [ 8019, -45, 0, 0, 3, -6, -1, 0, 0, -E(7)-E(7)^2-E(7)^4, -E(7)^3-E(7)^5-E(7)^6, -1, 0, 0, 0, 0, 0, 0,
      -E(7)-E(7)^2-E(7)^4, -E(7)^3-E(7)^5-E(7)^6, 0, 0, 0, 0 ] ), Character( CharacterTable( "McL" ), [ 8019, -45, 0, 0, 3, -6, -1, 0, 0,
      -E(7)^3-E(7)^5-E(7)^6, -E(7)-E(7)^2-E(7)^4, -1, 0, 0, 0, 0, 0, 0, -E(7)^3-E(7)^5-E(7)^6, -E(7)-E(7)^2-E(7)^4, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 8250, 10, 15, 6, -2, 0, 0, -5, -2, -E(7)-E(7)^2-E(7)^4, -E(7)^3-E(7)^5-E(7)^6, 0, 0, 0, 0, 0, 0, 1,
      E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6, 0, 0, 0, 0 ] ), Character( CharacterTable( "McL" ), [ 8250, 10, 15, 6, -2, 0, 0, -5, -2,
      -E(7)^3-E(7)^5-E(7)^6, -E(7)-E(7)^2-E(7)^4, 0, 0, 0, 0, 0, 0, 1, E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 9625, 105, 40, -5, -3, 0, 0, 0, 3, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 9856, 0, -80, -8, 0, 6, 1, 0, 0, 0, 0, 0, 2*E(3)-E(3)^2, -E(3)+2*E(3)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 9856, 0, -80, -8, 0, 6, 1, 0, 0, 0, 0, 0, -E(3)+2*E(3)^2, 2*E(3)-E(3)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ),
  Character( CharacterTable( "McL" ), [ 10395, -21, 27, 0, -1, -5, 0, 3, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -E(15)^7-E(15)^11-E(15)^13-E(15)^14,
      -E(15)-E(15)^2-E(15)^4-E(15)^8, E(15)^7+E(15)^11+E(15)^13+E(15)^14, E(15)+E(15)^2+E(15)^4+E(15)^8 ] ), Character( CharacterTable( "McL" ),
    [ 10395, -21, 27, 0, -1, -5, 0, 3, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -E(15)-E(15)^2-E(15)^4-E(15)^8, -E(15)^7-E(15)^11-E(15)^13-E(15)^14,
      E(15)+E(15)^2+E(15)^4+E(15)^8, E(15)^7+E(15)^11+E(15)^13+E(15)^14 ] ) ]

External links

• McL on the Atlas of Finite Groups