Linear representation theory of McLaughlin group

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.

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 ] ) ]