Linear representation theory of projective general linear group:PGL(2,7)

GAP implementation
The degrees of irreducible representations can be computed using GAP's CharacterDegrees function:

gap> CharacterDegrees(PGL(2,7)); [ [ 1, 2 ], [ 6, 3 ], [ 7, 2 ], [ 8, 2 ] ]

The character table can be computed using GAP's Irr and CharacterTable functions:

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