/* www-ATLAS of Group Representations. O8+(3) represented as permutations on 1080 points. */ G:=PermutationGroup<1080|\[ 2,1,4,3,7,9,5,12,6,14,16,8,19,10,22,11,25,27,13,30,32,15,35,36,17, 39,18,41,42,20,45,21,47,49,23,24,53,55,26,58,28,29,56,62,31,65,33,68,34,71, 73,75,37,78,38,43,81,40,83,85,87,44,90,92,46,95,97,48,100,101,50,104,51,107,52, 110,112,54,115,89,57,117,59,120,60,123,61,126,80,63,129,64,132,134,66,137,67,140,142,69, 70,145,147,72,150,151,74,154,155,76,156,77,148,159,79,162,82,164,166,84,169,171,86,173,175, 88,178,180,91,182,183,93,186,94,189,191,96,193,194,98,197,99,200,202,102,205,103,113,207,105, 106,211,213,108,109,111,218,220,114,223,225,116,227,118,230,119,233,235,121,237,122,239,124,242,125, 244,246,127,249,128,250,130,131,252,254,133,255,256,135,259,136,261,138,139,265,267,141,263,270,143, 273,144,276,278,146,281,149,282,284,286,152,289,153,292,294,296,298,157,301,158,303,304,160,307,161, 310,163,313,315,165,318,319,167,322,168,325,170,327,172,330,332,174,334,176,337,177,340,341,179,181, 345,184,348,185,187,188,352,354,190,356,192,358,198,361,195,364,196,366,368,199,371,372,201,375,376, 203,378,204,380,381,206,208,383,209,386,210,389,388,212,349,392,214,395,215,397,216,400,217,402,404, 219,407,221,222,411,413,224,415,416,226,419,420,228,423,229,426,428,231,232,432,434,234,437,438,236, 440,238,442,338,240,446,241,448,243,450,451,245,329,454,247,248,457,459,461,251,464,466,253,290,445, 456,257,403,258,474,260,476,262,479,481,264,483,391,266,486,268,487,269,490,491,271,272,495,496,274, 275,499,277,501,279,280,503,283,505,506,285,509,288,287,512,363,291,516,518,293,521,295,523,504,297, 524,299,353,300,529,530,302,532,533,535,305,538,306,536,308,309,542,544,311,312,548,550,314,553,554, 316,556,317,558,560,561,320,563,321,566,568,323,324,571,326,574,328,577,519,350,331,492,333,581,335, 336,585,587,339,590,351,342,594,343,596,344,598,599,346,601,347,604,606,607,537,597,611,612,355,615, 357,618,619,359,621,360,623,362,500,625,365,367,628,629,369,370,447,634,635,373,374,639,641,377,484, 379,644,382,399,384,385,522,650,387,653,654,390,624,588,657,393,636,394,444,661,396,507,398,401,666, 668,614,540,405,406,672,408,409,676,410,414,470,412,682,528,684,417,687,418,608,689,690,421,693,422, 695,694,424,425,698,427,700,429,702,430,431,705,433,708,605,435,711,436,713,673,439,717,646,441,714, 665,443,723,724,660,449,728,730,732,452,734,453,514,737,455,740,664,691,458,745,460,471,462,463,647, 465,751,752,467,565,468,469,545,757,759,472,473,681,527,475,766,768,477,478,770,480,773,482,513,485, 775,777,488,489,781,783,785,658,493,494,517,790,675,497,735,498,703,794,502,796,573,600,800,802,508, 805,786,510,511,808,809,515,633,812,580,520,760,784,592,576,525,816,526,819,821,823,531,570,827,638, 534,830,832,706,834,613,539,710,541,836,838,543,839,546,547,593,709,549,552,551,810,845,555,847,557, 848,559,642,851,562,679,853,564,692,683,567,857,569,575,861,862,572,865,866,744,818,860,578,579,774, 870,787,582,873,583,874,584,877,586,640,879,589,882,884,591,886,887,888,720,595,892,893,771,867,891, 602,603,898,899,900,890,609,902,610,662,869,906,907,807,878,616,782,617,829,620,748,911,622,725,626, 913,627,903,916,814,630,767,631,663,632,652,727,910,919,637,921,923,924,643,926,645,908,875,929,648, 817,649,917,933,651,936,764,655,656,696,841,659,904,780,915,667,801,721,669,881,670,925,671,945,946, 948,674,951,769,677,954,678,956,680,957,685,959,686,688,949,811,961,952,963,697,965,699,701,966,880, 704,967,707,969,922,927,712,972,974,722,715,716,960,977,718,719,749,981,761,726,928,982,729,731,798, 985,733,765,736,850,820,738,987,739,989,741,742,743,992,756,750,746,747,995,958,997,998,753,754,755, 1001,758,778,813,1004,762,763,797,1006,788,772,1000,776,986,815,779,803,990,789,1010,791,855,792,793,822, 795,856,871,799,1012,1014,1015,804,1017,1019,806,1021,1022,1023,993,1024,975,1025,1027,824,825,1028,826,840,1030, 828,843,1031,831,1033,833,835,895,837,863,842,1035,844,973,846,849,852,1016,854,1041,1042,858,964,859,942, 988,864,1039,1045,1046,868,872,1048,1049,876,914,883,976,885,918,1036,889,940,1038,894,1052,896,897,1055,912, 901,1057,1050,905,1020,909,1018,1060,1061,920,1062,930,1063,931,932,968,934,1007,935,1005,937,938,939,941,943, 1070,944,947,1069,950,953,1071,955,1053,962,991,1043,994,978,1051,970,971,1037,1075,979,980,1068,983,984,1003, 1040,996,1034,1066,999,1065,1002,1067,1077,1008,1009,1011,1013,1074,1056,1054,1058,1047,1029,1026,1032,1079,1080,1064,1044, 1078,1059,1076,1072,1073] ,\[ 3,1,5,6,8,10,11,2,13,15,17,18,20,21,23,24,26,28,29,31,33,34,4,37,38, 40,9,39,43,44,27,46,48,50,51,52,54,56,57,7,59,60,61,63,64,66,67,69,70,72, 74,76,77,79,80,75,12,82,84,86,88,89,91,93,94,96,98,99,14,102,103,105,106,108,109, 111,113,114,16,116,35,118,119,121,122,124,125,19,127,128,130,131,133,135,136,138,139,141,71,143, 144,146,148,149,22,152,153,81,25,101,147,157,158,160,161,132,163,165,167,168,170,145,172,174,176, 177,179,181,123,30,184,185,187,188,190,90,192,32,195,196,198,199,201,203,204,206,36,68,208,209, 210,212,214,215,216,217,219,221,222,224,142,226,228,229,231,232,234,236,65,41,238,240,241,42,243, 245,247,248,207,180,95,251,183,253,55,178,45,257,258,169,260,262,263,264,266,268,269,47,271,272, 274,275,277,279,280,49,62,283,285,287,288,290,291,293,295,297,299,300,302,227,53,305,306,308,309, 311,312,314,316,317,58,320,321,323,324,282,326,328,329,331,175,333,335,336,338,339,334,342,343,344, 346,347,349,350,249,351,353,197,355,162,357,359,360,362,363,365,267,367,369,370,115,373,374,294,377, 276,110,379,85,361,225,382,384,385,387,388,390,391,154,73,393,394,396,100,398,399,383,401,403,405, 406,408,409,410,412,250,414,78,417,418,191,421,422,424,425,427,429,430,431,433,435,436,83,439,341, 441,211,443,444,445,129,447,449,448,173,452,453,87,455,420,456,458,460,462,463,465,467,468,92,469, 470,471,472,473,332,475,477,478,480,273,482,484,485,358,97,366,488,489,189,492,493,494,491,193,497, 498,500,378,438,356,502,120,504,104,507,508,510,511,426,513,514,515,517,519,520,107,522,289,376,495, 525,526,527,528,348,413,531,112,534,536,537,539,540,541,432,194,543,545,546,547,549,551,552,117,555, 265,557,233,559,397,261,562,564,565,567,569,446,570,572,573,575,576,578,579,580,529,556,126,582,583, 584,586,588,589,591,592,593,186,595,597,205,223,600,286,602,603,605,218,608,609,610,134,613,614,616, 617,319,499,620,137,622,461,624,416,389,626,627,140,630,631,632,633,459,636,637,638,640,606,619,642, 643,645,646,155,647,648,649,651,652,150,655,656,151,327,658,304,659,533,660,662,663,664,665,230,667, 669,156,670,671,235,673,674,675,677,678,679,680,681,159,683,685,686,281,688,481,411,691,692,220,694, 696,490,440,697,699,259,164,701,524,703,704,706,707,166,709,710,428,712,714,715,716,530,718,719,720, 721,722,171,725,726,727,729,731,598,733,735,732,736,738,739,741,742,743,744,746,747,255,748,749,544, 750,182,753,754,755,296,496,756,758,760,761,762,763,764,765,767,676,769,364,771,772,310,774,621,577, 776,778,779,780,782,784,200,786,787,788,789,657,705,791,792,793,202,795,400,797,798,799,801,803,804, 806,807,728,375,464,810,644,811,213,813,814,815,816,318,509,817,818,634,820,822,824,825,826,794,828, 829,831,833,516,419,628,835,301,542,837,623,501,345,840,841,734,625,842,821,843,844,604,846,848,849, 838,737,850,745,730,852,845,854,855,856,483,858,859,860,278,863,864,823,618,237,867,548,868,869,239, 871,805,872,242,607,875,876,878,340,244,880,881,883,717,885,246,325,889,890,891,371,894,790,601,895, 896,897,752,882,252,254,901,256,903,904,905,587,819,908,661,590,380,851,909,910,740,711,912,684,907, 827,914,915,836,635,402,917,770,423,918,270,713,911,920,451,922,654,877,925,927,928,802,808,930,931, 932,381,284,934,935,937,523,938,939,886,940,924,292,941,942,812,566,298,354,781,943,944,553,437,947, 949,950,952,953,693,303,955,892,956,958,538,307,887,450,960,870,962,906,313,964,785,853,315,865,967, 902,415,968,926,970,666,971,973,668,322,975,976,724,766,978,979,980,594,571,800,330,983,984,898,839, 612,963,888,879,337,986,554,988,535,479,990,991,921,993,723,913,884,994,996,599,874,466,999,700,1000, 695,1002,1003,352,1005,757,957,959,574,1007,629,1008,561,775,985,916,368,1009,768,372,585,893,641,521,1010, 982,687,834,1011,1013,690,945,1016,1018,965,1020,386,503,987,392,615,395,1026,404,506,946,1029,862,407,486, 1031,518,476,1032,974,1012,777,861,474,1034,702,1036,923,1004,581,1037,1038,1039,1040,434,1043,1044,1028,1041,682, 992,989,899,773,442,653,1047,981,1021,487,961,977,454,809,512,558,1050,457,639,1051,1025,1053,1054,751,857, 1056,919,1022,563,1058,969,1059,866,698,532,1060,796,505,1064,1065,1066,689,1057,1067,1068,1069,1024,1061,759,596, 550,873,568,1045,936,1019,966,1042,1017,1030,830,1072,560,1073,1001,1074,998,900,929,672,1046,708,997,951,948, 1070,1052,1076,1075,1062,1006,650,611,783,972,1078,933,1063,995,1023,1055,1049,1035,1027,1014,1071,954,847,832,1033, 1080,1077,1015,1079,1048] >; print "Group G is O8+(3) < Sym(1080)";