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