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 Size | 1 36 378 945 1260 168 2240 3360 756 7560 11340 11340 3024 2520 2520 7560 10080 10080 20160 30240 25920 45360 40320 9072 18144 15120 15120 25920 24192 18144 Order | 1 2 2 2 2 3 3 3 4 4 4 4 5 6 6 6 6 6 6 6 7 8 9 10 10 12 12 14 15 20 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- p = 2 1 1 1 1 1 6 7 8 3 3 3 4 13 6 6 6 8 8 7 8 21 12 23 13 13 16 16 21 29 24 p = 3 1 2 3 4 5 1 1 1 9 10 11 12 13 5 2 3 5 2 5 4 21 22 7 24 25 9 10 28 13 30 p = 5 1 2 3 4 5 6 7 8 9 10 11 12 1 14 15 16 17 18 19 20 21 22 23 3 2 26 27 28 6 9 p = 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 22 23 24 25 26 27 2 29 30 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- 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 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 X.3 + 8 6 4 0 2 5 -1 2 4 2 0 0 3 -1 3 1 2 0 -1 0 1 0 -1 -1 1 1 -1 -1 0 -1 X.4 + 8 -6 4 0 -2 5 -1 2 -4 2 0 0 3 1 -3 1 -2 0 1 0 1 0 -1 -1 -1 -1 -1 1 0 1 X.5 + 27 15 7 3 3 9 0 0 5 1 1 -1 2 3 3 1 0 0 0 0 -1 -1 0 2 0 -1 1 1 -1 0 X.6 + 27-15 7 3 -3 9 0 0 -5 1 -1 -1 2 -3 -3 1 0 0 0 0 -1 1 0 2 0 1 1 -1 -1 0 X.7 + 28 14 4 -4 -2 10 1 1 6 0 -2 0 3 -2 2 -2 1 -1 1 -1 0 0 1 -1 -1 0 0 0 0 1 X.8 + 28-14 4 -4 2 10 1 1 -6 0 2 0 3 2 -2 -2 -1 1 -1 -1 0 0 1 -1 1 0 0 0 0 -1 X.9 + 42 0 2 -6 0 -6 6 0 0 -2 0 2 2 0 0 2 0 0 0 0 0 0 0 2 0 0 -2 0 -1 0 X.10 + 42 14 6 2 2 0 -3 3 -4 0 0 2 -3 2 2 0 -1 -1 -1 -1 0 0 0 1 -1 2 0 0 0 1 X.11 + 42-14 6 2 -2 0 -3 3 4 0 0 2 -3 -2 -2 0 1 1 1 -1 0 0 0 1 1 -2 0 0 0 -1 X.12 + 48 20 8 0 4 6 3 0 0 0 0 0 -2 -2 2 2 -2 2 1 0 -1 0 0 -2 0 0 0 -1 1 0 X.13 + 48-20 8 0 -4 6 3 0 0 0 0 0 -2 2 -2 2 2 -2 -1 0 -1 0 0 -2 0 0 0 1 1 0 X.14 + 56 14 -4 0 -6 11 2 2 4 -2 0 0 1 3 -1 -1 0 2 0 0 0 0 -1 1 -1 1 1 0 1 -1 X.15 + 56-14 -4 0 6 11 2 2 -4 -2 0 0 1 -3 1 -1 0 -2 0 0 0 0 -1 1 1 -1 1 0 1 1 X.16 + 70 0 -10 6 0 10 -2 4 0 -2 0 -2 0 0 0 2 0 0 0 0 0 0 1 0 0 0 -2 0 0 0 X.17 + 84 14 4 4 -2 -6 3 3 -6 0 2 0 -1 -2 2 -2 1 -1 1 1 0 0 0 -1 -1 0 0 0 -1 -1 X.18 + 84-14 4 4 2 -6 3 3 6 0 -2 0 -1 2 -2 -2 -1 1 -1 1 0 0 0 -1 1 0 0 0 -1 1 X.19 + 105 35 5 1 -1 15 -3 -3 5 -1 1 1 0 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 -1 -1 0 0 0 X.20 + 105-35 5 1 1 15 -3 -3 -5 -1 -1 1 0 1 1 -1 1 1 1 1 0 -1 0 0 0 1 -1 0 0 0 X.21 + 120 20 0 8 4 0 3 -3 0 0 0 0 0 4 -4 0 1 -1 1 -1 1 0 0 0 0 0 0 -1 0 0 X.22 + 120-20 0 8 -4 0 3 -3 0 0 0 0 0 -4 4 0 -1 1 -1 -1 1 0 0 0 0 0 0 1 0 0 X.23 + 162 36 6 -6 0 0 0 0 -6 0 -2 -2 -3 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 -1 X.24 + 162-36 6 -6 0 0 0 0 6 0 2 -2 -3 0 0 0 0 0 0 0 1 0 0 1 -1 0 0 -1 0 1 X.25 + 168 14 4 0 2 -15 -3 0 -4 -2 0 0 3 -1 -1 1 2 2 -1 0 0 0 0 -1 -1 -1 1 0 0 1 X.26 + 168-14 4 0 -2 -15 -3 0 4 -2 0 0 3 1 1 1 -2 -2 1 0 0 0 0 -1 1 1 1 0 0 -1 X.27 + 189 21 -11 -3 -3 9 0 0 1 1 1 1 -1 -3 -3 1 0 0 0 0 0 -1 0 -1 1 1 1 0 -1 1 X.28 + 189-21 -11 -3 3 9 0 0 -1 1 -1 1 -1 3 3 1 0 0 0 0 0 1 0 -1 -1 -1 1 0 -1 -1 X.29 + 216 6 -4 0 -6 -9 0 0 -4 2 0 0 1 3 3 -1 0 0 0 0 -1 0 0 1 1 -1 -1 -1 1 1 X.30 + 216 -6 -4 0 6 -9 0 0 4 2 0 0 1 -3 -3 -1 0 0 0 0 -1 0 0 1 -1 1 -1 1 1 -1