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