Linear representation theory of Mathieu group:M11

Degrees of irreducible representations
The degrees of irreducible representations can be computed using the CharacterDegrees, CharacterTable, and MathieuGroup functions:

gap> CharacterDegrees(CharacterTable(MathieuGroup(11))); [ [ 1, 1 ], [ 10, 3 ], [ 11, 1 ], [ 16, 2 ], [ 44, 1 ], [ 45, 1 ], [ 55, 1 ] ]

Character table
The character table can be computed using the Irr, CharacterTable, and MathieuGroup functions:

gap> Irr(CharacterTable(MathieuGroup(11))); [ Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ), [ 10, 0, 0, 2, 2, 0, -1, 1, -1, -1 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ), [ 10, -E(8)-E(8)^3, E(8)+E(8)^3, 0, -2, 0, 1, 1, -1, -1 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ), [ 10, E(8)+E(8)^3, -E(8)-E(8)^3, 0, -2, 0, 1, 1, -1, -1 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ), [ 11, -1, -1, -1, 3, 1, 0, 2, 0, 0 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ),   [ 16, 0, 0, 0, 0, 1, 0, -2, 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 ] ), Character( CharacterTable( Group(    [ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ), [ 16, 0, 0, 0, 0, 1, 0, -2, 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 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ),    [ 44, 0, 0, 0, 4, -1, 1, -1, 0, 0 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ),    [ 45, -1, -1, 1, -3, 0, 0, 0, 1, 1 ] ), Character( CharacterTable( Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]) ),    [ 55, 1, 1, -1, -1, 0, -1, 1, 0, 0 ] ) ]