Character Table --------------- ------------------------------------------------------------------ Class | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Size | 1 21 105 105 70 280 210 630 504 210 420 840 720 504 420 Order | 1 2 2 2 3 3 4 4 5 6 6 6 7 10 12 ------------------------------------------------------------------ p = 2 1 1 1 1 5 6 3 3 9 5 5 6 13 9 10 p = 3 1 2 3 4 1 1 7 8 9 3 2 4 13 14 7 p = 5 1 2 3 4 5 6 7 8 1 10 11 12 13 2 15 p = 7 1 2 3 4 5 6 7 8 9 10 11 12 1 14 15 ------------------------------------------------------------------ X.1 + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 + 1 -1 1 -1 1 1 -1 1 1 1 -1 -1 1 -1 -1 X.3 + 6 4 2 0 3 0 2 0 1 -1 1 0 -1 -1 -1 X.4 + 6 -4 2 0 3 0 -2 0 1 -1 -1 0 -1 1 1 X.5 + 14 4 2 0 -1 2 -2 0 -1 -1 1 0 0 -1 1 X.6 + 14 6 2 2 2 -1 0 0 -1 2 0 -1 0 1 0 X.7 + 14 -6 2 -2 2 -1 0 0 -1 2 0 1 0 -1 0 X.8 + 14 -4 2 0 -1 2 2 0 -1 -1 -1 0 0 1 -1 X.9 + 15 5 -1 -3 3 0 1 -1 0 -1 -1 0 1 0 1 X.10 + 15 -5 -1 3 3 0 -1 -1 0 -1 1 0 1 0 -1 X.11 + 20 0 -4 0 2 2 0 0 0 2 0 0 -1 0 0 X.12 + 21 1 1 -3 -3 0 -1 -1 1 1 1 0 0 1 -1 X.13 + 21 -1 1 3 -3 0 1 -1 1 1 -1 0 0 -1 1 X.14 + 35 5 -1 1 -1 -1 -1 1 0 -1 -1 1 0 0 -1 X.15 + 35 -5 -1 -1 -1 -1 1 1 0 -1 1 -1 0 0 1