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