Character Table --------------- ------------------------------------------------------------------------------------- Class | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Size | 1 1 12 12 12 12 18 72 16 32 32 12 36 36 72 72 16 32 32 96 96 96 96 144 96 Order | 1 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 6 6 6 6 6 6 6 8 12 ------------------------------------------------------------------------------------- p = 2 1 1 1 1 1 1 1 1 9 10 11 2 7 7 7 7 9 11 10 10 11 10 11 12 17 p = 3 1 2 3 4 5 6 7 8 1 1 1 12 13 14 15 16 2 2 2 5 4 6 3 24 12 ------------------------------------------------------------------------------------- X.1 + 1 1 1 1 1 1 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 1 -1 1 -1 1 -1 1 X.3 + 1 1 -1 -1 1 1 1 -1 1 1 1 1 -1 -1 1 -1 1 1 1 1 -1 1 -1 -1 1 X.4 + 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 X.5 + 2 2 0 0 2 2 2 0 -1 -1 2 2 0 0 2 0 -1 2 -1 -1 0 -1 0 0 -1 X.6 + 2 2 0 0 -2 -2 2 0 -1 -1 2 2 0 0 -2 0 -1 2 -1 1 0 1 0 0 -1 X.7 + 2 2 2 2 0 0 2 0 -1 2 -1 2 0 0 0 2 -1 -1 2 0 -1 0 -1 0 -1 X.8 + 2 2 -2 -2 0 0 2 0 -1 2 -1 2 0 0 0 -2 -1 -1 2 0 1 0 1 0 -1 X.9 + 4 -4 -2 2 2 -2 0 0 -2 1 1 0 2 -2 0 0 2 -1 -1 -1 -1 1 1 0 0 X.10 + 4 -4 2 -2 2 -2 0 0 -2 1 1 0 -2 2 0 0 2 -1 -1 -1 1 1 -1 0 0 X.11 + 4 -4 -2 2 -2 2 0 0 -2 1 1 0 -2 2 0 0 2 -1 -1 1 -1 -1 1 0 0 X.12 + 4 -4 2 -2 -2 2 0 0 -2 1 1 0 2 -2 0 0 2 -1 -1 1 1 -1 -1 0 0 X.13 + 4 4 0 0 0 0 4 0 1 -2 -2 4 0 0 0 0 1 -2 -2 0 0 0 0 0 1 X.14 + 6 6 0 0 0 0 -2 2 3 0 0 2 -2 -2 0 0 3 0 0 0 0 0 0 0 -1 X.15 + 6 6 0 0 0 0 -2 -2 3 0 0 2 2 2 0 0 3 0 0 0 0 0 0 0 -1 X.16 + 8 -8 0 0 4 -4 0 0 2 -1 2 0 0 0 0 0 -2 -2 1 1 0 -1 0 0 0 X.17 + 8 -8 -4 4 0 0 0 0 2 2 -1 0 0 0 0 0 -2 1 -2 0 1 0 -1 0 0 X.18 + 8 -8 4 -4 0 0 0 0 2 2 -1 0 0 0 0 0 -2 1 -2 0 -1 0 1 0 0 X.19 + 8 -8 0 0 -4 4 0 0 2 -1 2 0 0 0 0 0 -2 -2 1 -1 0 1 0 0 0 X.20 + 9 9 3 3 3 3 1 1 0 0 0 -3 1 1 -1 -1 0 0 0 0 0 0 0 -1 0 X.21 + 9 9 -3 -3 3 3 1 -1 0 0 0 -3 -1 -1 -1 1 0 0 0 0 0 0 0 1 0 X.22 + 9 9 3 3 -3 -3 1 -1 0 0 0 -3 -1 -1 1 -1 0 0 0 0 0 0 0 1 0 X.23 + 9 9 -3 -3 -3 -3 1 1 0 0 0 -3 1 1 1 1 0 0 0 0 0 0 0 -1 0 X.24 + 12 12 0 0 0 0 -4 0 -3 0 0 4 0 0 0 0 -3 0 0 0 0 0 0 0 1 X.25 + 16-16 0 0 0 0 0 0 -2 -2 -2 0 0 0 0 0 2 2 2 0 0 0 0 0 0