Linear representation theory of symmetric group:S7

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

gap> CharacterDegrees(SymmetricGroup(7)); [ [ 1, 2 ], [ 6, 2 ], [ 14, 4 ], [ 15, 2 ], [ 20, 1 ], [ 21, 2 ], [ 35, 2 ] ]

The charaters of irreducible representations can be computed using GAP's CharacterTable function:

gap> Irr(CharacterTable(SymmetricGroup(7))); [ Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1 ] ), Character( CharacterTable( Sym(   [ 1 .. 7 ] ) ), [ 6, -4, 2, 0, 3, -1, -1, 0, -2, 0, 1, 1, 1, 0, -1 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ),    [ 14, -6, 2, -2, 2, 0, 2, -1, 0, 0, 0, -1, -1, 1, 0 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 14, -4, 2, 0, -1, -1, -1, 2, 2, 0, -1, -1,      1, 0, 0 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 15, -5, -1, 3, 3, 1, -1, 0, -1, -1, -1, 0, 0, 0, 1 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 35, -5, -1, -1, -1, 1, -1, -1, 1, 1, 1, 0, 0, -1, 0 ] ), Character( CharacterTable( Sym(   [ 1 .. 7 ] ) ), [ 21, -1, 1, 3, -3, -1, 1, 0, 1, -1, 1, 1, -1, 0, 0 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ),    [ 21, 1, 1, -3, -3, 1, 1, 0, -1, -1, -1, 1, 1, 0, 0 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 20, 0, -4, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0,      -1 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 35, 5, -1, 1, -1, -1, -1, -1, -1, 1, -1, 0, 0, 1, 0 ] ), Character( CharacterTable( Sym(    [ 1 .. 7 ] ) ), [ 14, 4, 2, 0, -1, 1, -1, 2, -2, 0, 1, -1, -1, 0, 0 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ),    [ 15, 5, -1, -3, 3, -1, -1, 0, 1, -1, 1, 0, 0, 0, 1 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 14, 6, 2, 2, 2, 0, 2, -1, 0, 0, 0, -1, 1,      -1, 0 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 6, 4, 2, 0, 3, 1, -1, 0, 2, 0, -1, 1, -1, 0, -1 ] ), Character( CharacterTable( Sym( [ 1 .. 7 ] ) ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ) ]