/* www-ATLAS of Group Representations. O7(3) represented as permutations on 1080 points. */ G:=PermutationGroup<1080|\[ 2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,26,28,11,31,12,34,36,14,39,41, 16,44,17,47,49,19,52,54,21,57,22,60,62,24,65,25,68,70,27,73,75,29,78,30,81, 83,32,86,33,88,90,35,92,94,37,97,38,100,102,40,105,106,42,109,43,112,114,45,117,46, 120,122,48,125,127,50,130,51,133,135,53,138,55,141,56,144,58,147,59,150,152,61,155,157,63, 160,64,163,165,66,67,169,171,69,174,176,71,179,72,182,184,74,187,188,76,190,77,193,195,79, 198,80,201,203,82,161,207,84,164,85,212,214,87,217,219,89,222,224,91,227,229,93,232,233,95, 236,96,239,241,98,243,99,246,248,101,131,252,103,134,104,257,259,261,107,263,108,266,268,110,271, 111,274,276,113,279,281,115,270,116,285,287,118,119,291,121,294,295,123,298,124,301,302,126,305,306, 128,247,129,311,313,315,132,318,312,283,321,136,286,137,326,328,139,331,140,334,336,142,338,143,340, 342,145,344,146,347,349,148,149,353,355,151,357,359,153,361,154,364,156,367,368,158,202,159,373,375, 376,162,378,380,345,382,166,348,167,385,168,389,170,392,394,172,397,173,400,183,175,374,402,177,405, 178,408,410,180,412,181,415,210,418,185,213,186,422,351,425,189,428,429,191,192,346,433,194,436,438, 196,197,377,443,199,200,447,448,450,452,204,209,205,456,206,458,459,208,462,464,211,467,360,441,471, 215,442,216,475,476,218,479,481,220,483,221,486,223,488,225,490,226,492,228,255,296,230,258,231,500, 289,503,234,506,235,509,237,512,238,323,240,514,516,242,518,520,244,245,523,525,526,466,249,272,250, 251,303,253,493,254,533,256,536,537,260,539,519,541,262,544,546,264,548,265,551,552,267,549,554,269, 494,273,559,560,275,563,565,277,568,278,571,280,573,574,282,576,578,284,581,530,584,288,557,588,290, 591,593,292,293,597,599,601,297,498,604,299,606,300,609,611,324,327,304,521,528,616,307,308,619,309, 622,310,625,627,628,314,631,316,317,634,636,319,639,320,642,372,322,610,645,647,325,650,632,653,329, 330,657,659,332,662,333,665,335,667,570,337,669,339,637,341,673,343,379,401,677,678,680,434,681,350, 670,685,352,687,689,354,691,693,356,695,686,358,697,362,700,363,703,365,387,366,444,671,369,561,370, 371,711,445,713,420,648,717,381,719,720,383,384,723,386,725,388,728,729,390,731,391,732,393,398,733, 395,396,736,399,738,740,423,742,403,404,524,745,406,747,407,750,752,409,755,485,411,758,413,414,759, 416,760,417,762,666,419,739,765,421,767,706,600,424,705,771,426,773,427,776,716,778,430,781,431,587, 432,785,787,435,715,437,789,790,439,468,440,794,782,676,798,446,799,801,449,803,805,451,807,808,453, 809,454,455,812,814,457,473,817,460,702,461,489,821,463,823,825,465,828,830,469,831,470,531,833,472, 813,836,474,838,840,842,477,844,478,672,846,480,708,749,482,580,484,853,487,501,522,660,491,860,862, 614,495,496,854,497,499,867,857,851,502,511,504,866,505,718,507,875,508,877,510,880,513,882,712,515, 885,635,517,887,589,586,855,663,756,869,527,699,529,893,605,595,532,690,534,535,770,900,538,792,540, 894,768,542,543,906,545,547,550,818,911,553,913,555,582,556,915,558,916,917,562,919,564,804,664,566, 824,567,923,924,569,709,926,572,575,577,928,579,930,932,583,886,585,727,922,721,590,937,592,938,796, 594,942,596,943,841,598,613,948,914,602,861,603,806,607,608,951,724,847,612,944,775,912,615,617,819, 618,865,620,748,621,788,623,624,626,961,826,629,651,630,963,946,633,734,800,968,638,970,640,751,641, 811,960,643,891,644,646,974,649,845,976,652,977,654,907,655,780,656,981,658,834,661,793,984,925,902, 684,889,668,679,707,983,683,990,969,674,786,675,955,991,802,688,682,986,710,910,993,994,941,995,692, 933,694,978,998,696,992,698,898,1001,701,766,704,1000,852,1006,829,1009,714,726,927,1011,1002,883,1012,722, 985,850,1005,918,1014,730,839,957,1018,870,735,797,737,784,741,743,744,904,746,1021,1023,769,753,754,849, 757,895,761,959,763,1027,764,876,1030,1031,1032,772,774,953,980,873,777,779,795,1008,816,1034,783,1036,1037, 791,1039,939,972,863,1028,908,1024,929,827,810,1042,815,1016,1045,1046,996,820,859,822,1051,954,1053,832,1054, 835,837,878,1007,940,843,987,856,848,901,868,982,1017,1057,858,864,881,871,872,874,967,1043,879,1058,888, 884,897,1029,1061,903,890,979,945,892,1063,896,899,1064,905,1049,964,988,909,1050,1026,920,1067,921,958,1041, 1020,931,956,1003,934,935,936,1071,947,1048,949,950,1052,952,1072,1025,962,997,1074,965,966,1059,1035,1015,1019, 971,1038,973,975,1076,1078,989,999,1047,1070,1004,1066,1010,1013,1068,1062,1022,1065,1073,1060,1033,1040,1069,1044,1077, 1055,1075,1056,1080,1079] ,\[ 3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,32,33,35,37,38,40,42, 43,45,46,48,50,51,53,55,56,58,59,61,63,64,66,67,69,71,72,74,76,77,79,80,82, 84,85,1,87,89,88,91,93,95,96,98,99,101,103,104,2,107,108,110,111,113,115,116,118,119, 121,123,124,126,128,129,131,132,134,136,137,139,140,142,143,145,146,148,149,151,153,154,156,158,159, 161,162,164,166,167,168,170,172,173,175,177,178,180,181,183,185,186,5,189,133,191,192,194,196,197, 199,200,202,204,205,206,208,209,210,211,213,215,216,218,220,221,223,225,226,228,230,231,7,234,235, 237,238,240,105,242,244,245,247,249,250,251,253,254,255,256,258,260,262,100,264,265,267,269,270,272, 273,275,277,278,280,28,282,283,284,286,288,289,290,292,293,114,296,297,299,300,302,303,304,10,307, 308,309,310,312,314,316,317,75,319,320,322,323,324,325,327,329,330,332,333,335,193,337,339,122,341, 343,73,345,346,348,350,351,352,354,356,169,358,313,360,362,363,365,366,13,369,370,371,372,374,135, 377,57,379,233,381,383,384,385,386,387,388,390,391,393,395,396,398,399,376,401,367,15,403,404,406, 407,409,295,411,413,414,416,417,419,361,420,421,423,424,426,427,83,430,344,431,432,434,435,437,439, 440,441,442,444,445,446,287,449,451,453,380,454,455,457,276,18,460,461,463,465,466,468,469,470,472, 36,473,474,342,477,478,480,482,201,484,485,487,305,20,489,318,491,493,494,495,496,497,498,499,501, 502,504,505,507,508,510,511,326,375,402,513,515,203,517,519,521,522,471,524,464,527,281,520,528,529, 530,23,429,531,532,534,535,452,500,538,540,467,542,543,545,165,547,549,550,382,488,514,553,555,556, 557,558,408,561,562,564,566,567,569,570,518,572,26,575,573,577,579,580,582,583,585,586,587,589,590, 592,594,595,596,598,600,602,539,603,551,605,607,608,610,268,612,613,588,614,615,617,618,241,620,621, 623,624,626,405,629,630,632,574,633,635,637,638,640,641,31,643,97,644,646,648,649,651,652,654,655, 656,658,660,661,663,664,666,436,34,668,394,670,671,378,672,674,294,675,676,252,679,616,677,682,683, 684,619,686,688,364,690,692,694,662,696,422,523,698,699,701,702,704,705,373,685,706,707,552,708,709, 710,712,236,714,715,716,279,718,39,642,721,722,581,724,726,727,509,730,141,673,516,669,697,41,734, 735,443,737,147,739,741,536,503,743,397,744,81,746,748,749,751,753,754,756,541,757,565,736,475,713, 400,425,761,44,763,65,764,227,766,768,537,769,723,770,772,634,774,775,777,229,779,780,782,720,783, 784,786,544,788,291,628,47,791,152,792,793,795,796,797,593,285,800,604,802,804,806,650,49,263,232, 448,810,811,813,815,816,591,818,130,819,820,90,822,359,824,826,827,829,160,821,533,832,52,834,331, 835,759,837,839,841,843,568,711,459,845,847,848,54,849,850,851,852,854,855,856,857,858,859,861,863, 678,864,865,862,866,647,868,506,869,155,870,447,871,872,873,874,876,144,878,879,881,353,347,883,884, 60,762,886,548,311,680,888,889,890,760,891,62,892,894,895,738,896,897,898,899,846,901,902,392,368, 903,904,905,188,907,908,266,909,910,912,438,68,102,914,880,799,882,259,807,918,481,920,70,921,922, 906,805,867,830,578,925,450,916,86,927,790,929,931,933,840,785,934,127,935,695,936,182,893,939,940, 941,483,778,944,945,946,947,949,913,659,224,950,665,636,462,952,953,355,222,78,954,691,955,928,956, 667,957,958,959,733,750,960,157,525,765,817,476,609,962,964,965,966,584,967,969,526,755,948,120,971, 773,171,700,972,973,787,747,975,930,758,653,740,838,978,979,980,321,825,982,983,174,798,985,986,687, 987,988,803,974,433,923,989,853,106,479,138,428,693,92,492,992,176,917,554,239,163,717,257,198,996, 94,997,995,187,999,994,599,1000,1002,1003,932,1004,1005,808,1007,1008,248,246,1010,109,731,212,298,1013,745, 357,512,559,844,1015,977,1016,1017,900,823,601,719,1019,301,418,214,833,752,1020,1022,1024,571,794,725,112, 970,1025,976,1026,924,887,1028,1029,771,117,926,828,546,729,338,911,306,336,340,1033,919,1035,486,179,1038, 742,415,1037,125,1014,1001,625,1040,334,1041,606,456,1043,1044,597,1047,1048,1049,1050,1027,1051,1052,1023,1045,349, 576,315,1055,1056,1036,1012,410,622,563,261,984,1011,1057,732,389,877,243,991,150,611,963,885,801,1030,1059, 942,981,1060,915,1039,781,1062,217,1053,639,219,937,951,860,1065,1066,689,681,776,1009,657,1018,1021,1068,645, 938,767,1069,184,836,1070,703,631,1042,190,458,195,1067,271,490,274,789,1073,814,943,1063,961,207,1075,1034, 812,842,1006,809,1077,1064,1061,728,560,993,998,1054,831,627,1031,990,1046,412,1078,1058,1079,968,1074,1080,1071, 1072,328,1032,1076,875] >; print "Group G is O7(3) < Sym(1080)";