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