Linear representation theory of projective special linear group:PSL(3,4)

Degrees of irreducible representations
The degrees of irreducible representations can be computed using GAP's CharacterDegrees, CharacterTable, and PSL functions:

gap> CharacterDegrees(CharacterTable(PSL(3,4))); [ [ 1, 1 ], [ 20, 1 ], [ 35, 3 ], [ 45, 2 ], [ 63, 2 ], [ 64, 1 ] ]

Character table
The character table can be computed using GAP's CharacterDegrees, CharacterTable, and PSL functions:

gap> Irr(CharacterTable(PSL(3,4))); [ Character( CharacterTable( Group([ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)    ]) ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19),      (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ), [ 20, -1, -1, 0, 0, 0, 4, 2, 0, 0 ] ), Character( CharacterTable( Group(    [ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ),    [ 35, 0, 0, 0, 0, 3, 3, -1, -1, -1 ] ), Character( CharacterTable( Group([ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19),      (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ), [ 35, 0, 0, 0, 0, -1, 3, -1, -1, 3 ] ), Character( CharacterTable( Group(    [ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ), [ 35, 0, 0, 0, 0, -1, 3, -1, 3, -1 ] ), Character( CharacterTable( Group([ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ), [ 45, E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4, 0, 0, 1, -3, 0, 1, 1 ] ), Character( CharacterTable( Group([ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ), [ 45, E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6, 0, 0, 1, -3, 0, 1, 1 ] ), Character( CharacterTable( Group( [ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ),   [ 63, 0, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3, -1, -1, 0, -1, -1 ] ), Character( CharacterTable( Group( [ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ),   [ 63, 0, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4, -1, -1, 0, -1, -1 ] ), Character( CharacterTable( Group( [ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12) ]) ),   [ 64, 1, 1, -1, -1, 0, 0, 1, 0, 0 ] ) ]