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