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 36 45 270 540 80 240 480 540 540 1620 3240 5184 720 1440 1440 1440 1440 2160 4320 6480 5760 5184 4320 4320 Order | 1 2 2 2 2 3 3 3 4 4 4 4 5 6 6 6 6 6 6 6 8 9 10 12 12 ----------------------------------------------------------------------------------------------------------------------- p = 2 1 1 1 1 1 6 7 8 3 4 4 4 13 6 7 7 8 8 7 8 9 22 13 19 14 p = 3 1 2 3 4 5 1 1 1 9 10 11 12 13 3 3 2 3 2 4 5 21 6 23 10 9 p = 5 1 2 3 4 5 6 7 8 9 10 11 12 1 14 15 16 17 18 19 20 21 22 2 24 25 ----------------------------------------------------------------------------------------------------------------------- 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 + 6 4 -2 2 0 -3 3 0 2 -2 2 0 1 1 1 1 -2 -2 -1 0 0 0 -1 1 -1 X.4 + 6 -4 -2 2 0 -3 3 0 2 2 -2 0 1 1 1 -1 -2 2 -1 0 0 0 1 -1 -1 X.5 + 10 0 -6 2 0 1 -2 4 2 0 0 -2 0 -3 0 0 0 0 2 0 0 1 0 0 -1 X.6 + 15 -5 7 3 -1 -3 0 3 -1 -3 1 1 0 1 -2 -2 1 1 0 -1 1 0 0 0 -1 X.7 + 15 -5 -1 -1 3 6 3 0 3 -1 -1 -1 0 2 -1 1 2 -2 -1 0 1 0 0 -1 0 X.8 + 15 5 7 3 1 -3 0 3 -1 3 -1 1 0 1 -2 2 1 -1 0 1 -1 0 0 0 -1 X.9 + 15 5 -1 -1 -3 6 3 0 3 1 1 -1 0 2 -1 -1 2 2 -1 0 -1 0 0 1 0 X.10 + 20 10 4 4 2 2 5 -1 0 2 2 0 0 -2 1 1 1 1 1 -1 0 -1 0 -1 0 X.11 + 20-10 4 4 -2 2 5 -1 0 -2 -2 0 0 -2 1 -1 1 -1 1 1 0 -1 0 1 0 X.12 + 20 0 4 -4 0 -7 2 2 4 0 0 0 0 1 -2 0 -2 0 2 0 0 -1 0 0 1 X.13 + 24 4 8 0 4 6 0 3 0 0 0 0 -1 2 2 -2 -1 1 0 1 0 0 -1 0 0 X.14 + 24 -4 8 0 -4 6 0 3 0 0 0 0 -1 2 2 2 -1 -1 0 -1 0 0 1 0 0 X.15 + 30-10-10 2 2 3 3 3 -2 4 0 0 0 -1 -1 -1 -1 -1 -1 -1 0 0 0 1 1 X.16 + 30 10-10 2 -2 3 3 3 -2 -4 0 0 0 -1 -1 1 -1 1 -1 1 0 0 0 -1 1 X.17 + 60 10 -4 4 2 6 -3 -3 0 -2 -2 0 0 2 -1 1 -1 1 1 -1 0 0 0 1 0 X.18 + 60-10 -4 4 -2 6 -3 -3 0 2 2 0 0 2 -1 -1 -1 -1 1 1 0 0 0 -1 0 X.19 + 60 0 12 4 0 -3 -6 0 4 0 0 0 0 -3 0 0 0 0 -2 0 0 0 0 0 1 X.20 + 64 16 0 0 0 -8 4 -2 0 0 0 0 -1 0 0 -2 0 -2 0 0 0 1 1 0 0 X.21 + 64-16 0 0 0 -8 4 -2 0 0 0 0 -1 0 0 2 0 2 0 0 0 1 -1 0 0 X.22 + 80 0-16 0 0-10 -4 2 0 0 0 0 0 2 2 0 2 0 0 0 0 -1 0 0 0 X.23 + 81 9 9 -3 -3 0 0 0 -3 3 -1 -1 1 0 0 0 0 0 0 0 1 0 -1 0 0 X.24 + 81 -9 9 -3 3 0 0 0 -3 -3 1 -1 1 0 0 0 0 0 0 0 -1 0 1 0 0 X.25 + 90 0 -6 -6 0 9 0 0 2 0 0 2 0 -3 0 0 0 0 0 0 0 0 0 0 -1