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 Size | 1 1 5 5 10 10 20 20 60 60 60 60 80 20 20 60 60 60 60 120 120 240 240 384 80 80 80 160 160 160 160 240 240 384 160 160 Order | 1 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 5 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 1 13 6 6 3 6 6 3 6 6 9 9 24 13 13 13 13 13 13 13 16 16 24 26 26 p = 3 1 2 3 4 5 6 7 8 9 10 11 12 1 14 15 16 17 18 19 20 21 22 23 24 5 6 2 3 8 7 4 32 33 34 15 14 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 2 35 36 --------------------------------------------------------------------------------------------------------------------------------- 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 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 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 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 X.5 + 4 4 4 4 4 4 2 2 0 2 0 2 1 2 2 0 2 2 0 0 0 0 0 -1 1 1 1 1 -1 -1 1 0 0 -1 -1 -1 X.6 + 4 4 4 4 4 4 -2 -2 0 -2 0 -2 1 -2 -2 0 -2 -2 0 0 0 0 0 -1 1 1 1 1 1 1 1 0 0 -1 1 1 X.7 + 4 -4 4-4 -4 4 -2 2 0 2 0 -2 1 -2 2 0 2 -2 0 0 0 0 0 -1 -1 1 -1 1 -1 1 -1 0 0 1 -1 1 X.8 + 4 -4 4-4 -4 4 2 -2 0 -2 0 2 1 2 -2 0 -2 2 0 0 0 0 0 -1 -1 1 -1 1 1 -1 -1 0 0 1 1 -1 X.9 + 5 5-3-3 1 1 -3 -3 1 1 1 1 2 3 3 1 -1 -1 1 -1 -1 -1 -1 0 -2 -2 2 0 0 0 0 1 1 0 0 0 X.10 + 5 5-3-3 1 1 3 3 1 -1 1 -1 2 -3 -3 1 1 1 1 -1 -1 1 1 0 -2 -2 2 0 0 0 0 -1 -1 0 0 0 X.11 + 5 5 5 5 5 5 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 -1 -1 0 -1 -1 -1 -1 1 1 -1 -1 -1 0 1 1 X.12 + 5 5 5 5 5 5 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 1 1 0 -1 -1 -1 -1 -1 -1 -1 1 1 0 -1 -1 X.13 + 5 -5-3 3 -1 1 3 -3 1 1 -1 -1 2 -3 3 1 -1 1 -1 1 -1 -1 1 0 2 -2 -2 0 0 0 0 1 -1 0 0 0 X.14 + 5 -5-3 3 -1 1 -3 3 1 -1 -1 1 2 3 -3 1 1 -1 -1 1 -1 1 -1 0 2 -2 -2 0 0 0 0 -1 1 0 0 0 X.15 + 5 -5 5-5 -5 5 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 0 1 -1 1 -1 1 -1 1 -1 1 0 1 -1 X.16 + 5 -5 5-5 -5 5 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 0 1 -1 1 -1 -1 1 1 1 -1 0 -1 1 X.17 + 6 6 6 6 6 6 0 0 -2 0 -2 0 0 0 0 -2 0 0 -2 -2 -2 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 X.18 + 6 -6 6-6 -6 6 0 0 -2 0 2 0 0 0 0 -2 0 0 2 2 -2 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 X.19 + 10 10-6-6 2 2 0 0 2 0 2 0 -2 0 0 2 0 0 2 -2 -2 0 0 0 2 2 -2 0 0 0 0 0 0 0 0 0 X.20 + 10-10-6 6 -2 2 0 0 2 0 -2 0 -2 0 0 2 0 0 -2 2 -2 0 0 0 -2 2 2 0 0 0 0 0 0 0 0 0 X.21 + 10-10 2-2 2 -2 -4 4 2 0 -2 0 1 -2 2 -2 -2 2 2 0 0 0 0 0 -1 1 -1 -1 1 -1 1 0 0 0 -1 1 X.22 + 10-10 2-2 2 -2 -2 2 -2 -2 2 2 1 -4 4 2 0 0 -2 0 0 0 0 0 -1 1 -1 -1 -1 1 1 0 0 0 1 -1 X.23 + 10-10 2-2 2 -2 2 -2 -2 2 2 -2 1 4 -4 2 0 0 -2 0 0 0 0 0 -1 1 -1 -1 1 -1 1 0 0 0 -1 1 X.24 + 10-10 2-2 2 -2 4 -4 2 0 -2 0 1 2 -2 -2 2 -2 2 0 0 0 0 0 -1 1 -1 -1 -1 1 1 0 0 0 1 -1 X.25 + 10 10 2 2 -2 -2 4 4 2 0 2 0 1 2 2 -2 -2 -2 -2 0 0 0 0 0 1 1 1 -1 1 1 -1 0 0 0 -1 -1 X.26 + 10 10 2 2 -2 -2 2 2 -2 -2 -2 -2 1 4 4 2 0 0 2 0 0 0 0 0 1 1 1 -1 -1 -1 -1 0 0 0 1 1 X.27 + 10 10 2 2 -2 -2 -2 -2 -2 2 -2 2 1 -4 -4 2 0 0 2 0 0 0 0 0 1 1 1 -1 1 1 -1 0 0 0 -1 -1 X.28 + 10 10 2 2 -2 -2 -4 -4 2 0 2 0 1 -2 -2 -2 2 2 -2 0 0 0 0 0 1 1 1 -1 -1 -1 -1 0 0 0 1 1 X.29 + 15 15-9-9 3 3 -3 -3 -1 1 -1 1 0 3 3 -1 -1 -1 -1 1 1 1 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 X.30 + 15 15-9-9 3 3 3 3 -1 -1 -1 -1 0 -3 -3 -1 1 1 -1 1 1 -1 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 X.31 + 15-15-9 9 -3 3 3 -3 -1 1 1 -1 0 -3 3 -1 -1 1 1 -1 1 1 -1 0 0 0 0 0 0 0 0 -1 1 0 0 0 X.32 + 15-15-9 9 -3 3 -3 3 -1 -1 1 1 0 3 -3 -1 1 -1 1 -1 1 -1 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 X.33 + 20-20 4-4 4 -4 2 -2 0 -2 0 2 -1 -2 2 0 2 -2 0 0 0 0 0 0 1 -1 1 1 1 -1 -1 0 0 0 -1 1 X.34 + 20-20 4-4 4 -4 -2 2 0 2 0 -2 -1 2 -2 0 -2 2 0 0 0 0 0 0 1 -1 1 1 -1 1 -1 0 0 0 1 -1 X.35 + 20 20 4 4 -4 -4 -2 -2 0 -2 0 -2 -1 2 2 0 2 2 0 0 0 0 0 0 -1 -1 -1 1 1 1 1 0 0 0 -1 -1 X.36 + 20 20 4 4 -4 -4 2 2 0 2 0 2 -1 -2 -2 0 -2 -2 0 0 0 0 0 0 -1 -1 -1 1 -1 -1 1 0 0 0 1 1