Linear representation theory of alternating group:A7

This article gives specific information, namely, linear representation theory, about a particular group, namely: alternating group:A7.
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Summary

Item	Value
degrees of irreducible representations over a splitting field	1,6,10,10,14,14,15,21,35 maximum: 35, lcm: 210, number: 9, sum of squares: 2520

GAP implementation

The degrees of irreducible representations can be computed using GAP's CharacterDegrees and AlternatingGroup functions:

gap> CharacterDegrees(AlternatingGroup(7));
[ [ 1, 1 ], [ 6, 1 ], [ 10, 2 ], [ 14, 2 ], [ 15, 1 ], [ 21, 1 ], [ 35, 1 ] ]

This means there is 1 degree 1 irreducible, 1 degree 6 irreducible, 2 degree 10 irreducibles, 2 degree 14 irreducibles, and 1 irreducible each of degrees 15, 21, 35.

The characters of irreducible representations can be computed using the CharacterTable function:

gap> Irr(CharacterTable(AlternatingGroup(7)));
[ Character( CharacterTable( Alt( [ 1 .. 7 ] ) ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Alt( [ 1 .. 7 ] ) ),
    [ 6, 2, 3, -1, 0, 0, 1, -1, -1 ] ), Character( CharacterTable( Alt( [ 1 .. 7 ] ) ), [ 10, -2, 1, 1, 1, 0, 0, E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4
     ] ), Character( CharacterTable( Alt( [ 1 .. 7 ] ) ), [ 10, -2, 1, 1, 1, 0, 0, E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6 ] ),
  Character( CharacterTable( Alt( [ 1 .. 7 ] ) ), [ 14, 2, 2, 2, -1, 0, -1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 7 ] ) ),
    [ 14, 2, -1, -1, 2, 0, -1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 7 ] ) ), [ 15, -1, 3, -1, 0, -1, 0, 1, 1 ] ),
  Character( CharacterTable( Alt( [ 1 .. 7 ] ) ), [ 21, 1, -3, 1, 0, -1, 1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 7 ] ) ),
    [ 35, -1, -1, -1, -1, 1, 0, 0, 0 ] ) ]