Character Table --------------- --------------------------------------------------------------------- Class | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Size | 1 5 10 20 60 60 80 20 60 60 120 240 384 80 160 160 240 160 Order | 1 2 2 2 2 2 3 4 4 4 4 4 5 6 6 6 8 12 --------------------------------------------------------------------- p = 2 1 1 1 1 1 1 7 3 2 3 3 6 13 7 7 7 9 14 p = 3 1 2 3 4 5 6 1 8 9 10 11 12 13 3 4 2 17 8 p = 5 1 2 3 4 5 6 7 8 9 10 11 12 1 14 15 16 17 18 --------------------------------------------------------------------- X.1 + 1 1 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 1 -1 -1 X.3 + 4 4 4 2 2 0 1 2 0 2 0 0 -1 1 -1 1 0 -1 X.4 + 4 4 4 -2 -2 0 1 -2 0 -2 0 0 -1 1 1 1 0 1 X.5 + 5-3 1 -3 1 1 2 3 1 -1 -1 -1 0 -2 0 0 1 0 X.6 + 5-3 1 3 -1 1 2 -3 1 1 -1 1 0 -2 0 0 -1 0 X.7 + 5 5 5 1 1 1 -1 1 1 1 1 -1 0 -1 1 -1 -1 1 X.8 + 5 5 5 -1 -1 1 -1 -1 1 -1 1 1 0 -1 -1 -1 1 -1 X.9 + 6 6 6 0 0 -2 0 0 -2 0 -2 0 1 0 0 0 0 0 X.10 + 10-6 2 0 0 2 -2 0 2 0 -2 0 0 2 0 0 0 0 X.11 + 10 2 -2 4 0 2 1 2 -2 -2 0 0 0 1 1 -1 0 -1 X.12 + 10 2 -2 2 -2 -2 1 4 2 0 0 0 0 1 -1 -1 0 1 X.13 + 10 2 -2 -2 2 -2 1 -4 2 0 0 0 0 1 1 -1 0 -1 X.14 + 10 2 -2 -4 0 2 1 -2 -2 2 0 0 0 1 -1 -1 0 1 X.15 + 15-9 3 -3 1 -1 0 3 -1 -1 1 1 0 0 0 0 -1 0 X.16 + 15-9 3 3 -1 -1 0 -3 -1 1 1 -1 0 0 0 0 1 0 X.17 + 20 4 -4 -2 -2 0 -1 2 0 2 0 0 0 -1 1 1 0 -1 X.18 + 20 4 -4 2 2 0 -1 -2 0 -2 0 0 0 -1 -1 1 0 1