Linear representation theory of Mathieu group:M10

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

gap> CharacterDegrees(CharacterTable(MathieuGroup(10))); [ [ 1, 2 ], [ 9, 2 ], [ 10, 3 ], [ 16, 1 ] ]

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

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