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 26 27 28 29 30 31 32 33 34 35 36 37 Size | 1 1 15 15 30 30 60 60 180 180 180 160 640 120 120 180 180 360 720 720 720 720 720 2304 160 480 480 640 960 960 1920 1920 1440 1440 2304 960 960 Order | 1 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 5 6 6 6 6 6 6 6 6 8 8 10 12 12 ----------------------------------------------------------------------------------------------------------------------------------------------------------- p = 2 1 1 1 1 1 1 1 1 1 1 1 12 13 4 4 3 3 3 10 10 4 10 10 24 12 12 12 13 12 12 13 13 17 16 24 27 27 p = 3 1 2 3 4 5 6 7 8 9 10 11 1 1 14 15 16 17 18 19 20 21 22 23 24 2 3 4 2 6 5 7 8 33 34 35 14 15 p = 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 25 26 27 28 29 30 31 32 33 34 2 36 37 ----------------------------------------------------------------------------------------------------------------------------------------------------------- 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 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 1 1 1 -1 -1 -1 -1 -1 1 1 -1 -1 X.3 + 5 5 5 5 1 1 -3 -3 1 1 1 -1 2 1 1 1 1 -3 -1 -1 1 -1 -1 0 -1 -1 -1 2 1 1 0 0 -1 -1 0 1 1 X.4 + 5 5 5 5 3 3 -1 -1 3 1 1 2 -1 3 3 1 1 -1 1 1 1 -1 -1 0 2 2 2 -1 0 0 -1 -1 1 -1 0 0 0 X.5 + 5 5 5 5 -3 -3 1 1 -3 1 1 2 -1 -3 -3 1 1 1 -1 -1 1 -1 -1 0 2 2 2 -1 0 0 1 1 -1 -1 0 0 0 X.6 + 5 5 5 5 -1 -1 3 3 -1 1 1 -1 2 -1 -1 1 1 3 1 1 1 -1 -1 0 -1 -1 -1 2 -1 -1 0 0 1 -1 0 -1 -1 X.7 + 6 -6 -2 2 -4 4 0 0 0 2 -2 3 0 2 -2 -2 2 0 -2 2 0 0 0 1 -3 1 -1 0 1 -1 0 0 0 0 -1 -1 1 X.8 + 6 -6 -2 2 4 -4 0 0 0 2 -2 3 0 -2 2 -2 2 0 2 -2 0 0 0 1 -3 1 -1 0 -1 1 0 0 0 0 -1 1 -1 X.9 + 9 9 9 9 3 3 3 3 3 1 1 0 0 3 3 1 1 3 -1 -1 1 1 1 -1 0 0 0 0 0 0 0 0 -1 1 -1 0 0 X.10 + 9 9 9 9 -3 -3 -3 -3 -3 1 1 0 0 -3 -3 1 1 -3 1 1 1 1 1 -1 0 0 0 0 0 0 0 0 1 1 -1 0 0 X.11 + 10 10 10 10 2 2 -2 -2 2 -2 -2 1 1 2 2 -2 -2 -2 0 0 -2 0 0 0 1 1 1 1 -1 -1 1 1 0 0 0 -1 -1 X.12 + 10 10 10 10 -2 -2 2 2 -2 -2 -2 1 1 -2 -2 -2 -2 2 0 0 -2 0 0 0 1 1 1 1 1 1 -1 -1 0 0 0 1 1 X.13 + 10-10 2 -2 -4 4 4 -4 0 2 -2 1 1 -2 2 2 -2 0 0 0 0 2 -2 0 -1 -1 1 -1 1 -1 1 -1 0 0 0 1 -1 X.14 + 10-10 2 -2 -4 4 -4 4 0 2 -2 1 1 -2 2 2 -2 0 0 0 0 -2 2 0 -1 -1 1 -1 1 -1 -1 1 0 0 0 1 -1 X.15 + 10-10 2 -2 4 -4 4 -4 0 2 -2 1 1 2 -2 2 -2 0 0 0 0 -2 2 0 -1 -1 1 -1 -1 1 1 -1 0 0 0 -1 1 X.16 + 10-10 2 -2 4 -4 -4 4 0 2 -2 1 1 2 -2 2 -2 0 0 0 0 2 -2 0 -1 -1 1 -1 -1 1 -1 1 0 0 0 -1 1 X.17 + 15 15 -1 -1 5 5 -3 -3 -3 -1 -1 3 0 1 1 3 3 1 1 1 -1 -1 -1 0 3 -1 -1 0 -1 -1 0 0 -1 1 0 1 1 X.18 + 15 15 -1 -1 7 7 3 3 -1 3 3 3 0 -1 -1 -1 -1 -1 1 1 -1 1 1 0 3 -1 -1 0 1 1 0 0 -1 -1 0 -1 -1 X.19 + 15 15 -1 -1 -7 -7 -3 -3 1 3 3 3 0 1 1 -1 -1 1 -1 -1 -1 1 1 0 3 -1 -1 0 -1 -1 0 0 1 -1 0 1 1 X.20 + 15 15 -1 -1 -5 -5 3 3 3 -1 -1 3 0 -1 -1 3 3 -1 -1 -1 -1 -1 -1 0 3 -1 -1 0 1 1 0 0 1 1 0 -1 -1 X.21 + 16 16 16 16 0 0 0 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 0 0 1 -2 -2 -2 -2 0 0 0 0 0 0 1 0 0 X.22 + 20-20 4 -4 0 0 0 0 0 -4 4 2 2 0 0 -4 4 0 0 0 0 0 0 0 -2 -2 2 -2 0 0 0 0 0 0 0 0 0 X.23 + 24-24 -8 8 -8 8 0 0 0 0 0 3 0 4 -4 0 0 0 0 0 0 0 0 -1 -3 1 -1 0 -1 1 0 0 0 0 1 1 -1 X.24 + 24-24 -8 8 8 -8 0 0 0 0 0 3 0 -4 4 0 0 0 0 0 0 0 0 -1 -3 1 -1 0 1 -1 0 0 0 0 1 -1 1 X.25 + 30 30 -2 -2 2 2 6 6 2 2 2 -3 0 -2 -2 2 2 -2 0 0 -2 0 0 0 -3 1 1 0 -1 -1 0 0 0 0 0 1 1 X.26 + 30 30 -2 -2 -2 -2 -6 -6 -2 2 2 -3 0 2 2 2 2 2 0 0 -2 0 0 0 -3 1 1 0 1 1 0 0 0 0 0 -1 -1 X.27 + 30-30-10 10 -4 4 0 0 0 2 -2 -3 0 2 -2 -2 2 0 2 -2 0 0 0 0 3 -1 1 0 1 -1 0 0 0 0 0 -1 1 X.28 + 30-30-10 10 4 -4 0 0 0 2 -2 -3 0 -2 2 -2 2 0 -2 2 0 0 0 0 3 -1 1 0 -1 1 0 0 0 0 0 1 -1 X.29 + 36-36-12 12 0 0 0 0 0 -4 4 0 0 0 0 4 -4 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 X.30 + 40-40 8 -8 -8 8 0 0 0 0 0 1 -2 -4 4 0 0 0 0 0 0 0 0 0 -1 -1 1 2 -1 1 0 0 0 0 0 -1 1 X.31 + 40-40 8 -8 8 -8 0 0 0 0 0 1 -2 4 -4 0 0 0 0 0 0 0 0 0 -1 -1 1 2 1 -1 0 0 0 0 0 1 -1 X.32 + 40-40 8 -8 0 0 -8 8 0 0 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 2 2 -2 -1 0 0 1 -1 0 0 0 0 0 X.33 + 40-40 8 -8 0 0 8 -8 0 0 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 2 2 -2 -1 0 0 -1 1 0 0 0 0 0 X.34 + 45 45 -3 -3 3 3 3 3 -5 -3 -3 0 0 3 3 1 1 -1 -1 -1 1 1 1 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 X.35 + 45 45 -3 -3 9 9 -3 -3 1 1 1 0 0 -3 -3 -3 -3 1 -1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 X.36 + 45 45 -3 -3 -9 -9 3 3 -1 1 1 0 0 3 3 -3 -3 -1 1 1 1 -1 -1 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 X.37 + 45 45 -3 -3 -3 -3 -3 -3 5 -3 -3 0 0 -3 -3 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0