Linear representation theory of Mathieu group:M10

This article gives specific information, namely, linear representation theory, about a particular group, namely: Mathieu group:M10.
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Summary

Item	Value
degrees of irreducible representations over a splitting field (such as ${\overline {\mathbb {Q} }}$ or $\mathbb {C}$)	1, 1, 9, 9, 10, 10, 10, 16 grouped form: 1 (2 times), 9 (2 times), 10 (3 times), 16 (1 time) maximum: 16, number: 8, lcm: 720, sum of squares: 720

GAP implementation

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 ] ) ]