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