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