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 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Size | 1 1 6 6 15 15 20 30 30 120 120 120 180 180 180 360 160 640 30 30 120 120 120 180 180 180 360 360 360 360 360 720 720 720 1440 1440 1440 2304 160 160 160 480 480 480 480 640 960 960 960 960 1280 3840 720 720 Order | 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8 8 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- p = 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 18 5 5 2 5 5 5 6 6 5 5 5 6 6 13 5 13 15 13 13 38 17 17 17 17 17 17 17 18 17 17 17 17 18 18 25 25 p = 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 1 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 7 2 7 6 4 3 5 2 9 10 12 8 7 11 53 54 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 24 25 26 27 28 29 30 31 32 33 34 35 36 37 1 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 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 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 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 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.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 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.5 + 5 5 -5 -5 5 5 -5 -1 -1 1 3 1 1 -1 1 -1 -1 2 1 1 -3 -1 -1 1 1 1 -1 -1 -3 3 -1 1 1 1 1 -1 -1 0 1 -1 1 -1 1 1 -1 2 -1 1 1 -1 -2 0 -1 -1 X.6 + 5 5 -5 -5 5 5 -5 -3 -3 3 1 3 1 -3 1 -1 2 -1 3 3 -1 -3 -3 3 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 -1 0 -2 2 -2 2 -2 -2 2 -1 0 0 0 0 1 1 1 1 X.7 + 5 5 -5 -5 5 5 -5 3 3 -3 -1 -3 1 3 1 -1 2 -1 -3 -3 1 3 3 -3 1 1 -1 -1 1 -1 -1 1 1 1 1 -1 -1 0 -2 2 -2 2 -2 -2 2 -1 0 0 0 0 1 -1 -1 -1 X.8 + 5 5 -5 -5 5 5 -5 1 1 -1 -3 -1 1 1 1 -1 -1 2 -1 -1 3 1 1 -1 1 1 -1 -1 3 -3 -1 -1 1 -1 1 1 -1 0 1 -1 1 -1 1 1 -1 2 1 -1 -1 1 -2 0 1 1 X.9 + 5 5 5 5 5 5 5 1 1 1 -3 1 1 1 1 1 -1 2 1 1 -3 1 1 1 1 1 1 1 -3 -3 1 -1 1 -1 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 2 1 1 1 1 2 0 -1 -1 X.10 + 5 5 5 5 5 5 5 3 3 3 -1 3 1 3 1 1 2 -1 3 3 -1 3 3 3 1 1 1 1 -1 -1 1 1 1 1 -1 1 -1 0 2 2 2 2 2 2 2 -1 0 0 0 0 -1 -1 1 1 X.11 + 5 5 5 5 5 5 5 -3 -3 -3 1 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