/* www-ATLAS of Group Representations. S6(3):2 represented as permutations on 1120 points. */ G:=PermutationGroup<1120|\[ 1,3,2,6,5,4,10,11,13,7,8,17,9,14,20,22,12,25,19,15,21,16,23,24,18, 26,34,36,37,39,31,41,43,27,45,28,29,49,30,52,32,54,33,57,35,46,56,48,38,63, 51,40,66,42,55,47,44,71,73,75,77,79,50,82,81,53,67,87,69,90,58,72,59,94,60, 97,61,78,62,100,65,64,104,84,106,86,68,88,110,70,112,114,116,74,119,120,76,123,125,80, 101,128,103,83,132,85,107,135,137,89,111,91,141,92,143,93,146,148,95,96,152,122,98,156,99, 159,161,102,164,165,131,105,169,171,108,173,109,138,177,179,113,182,115,185,186,117,147,118,190,181, 193,121,153,196,198,124,201,158,126,204,127,206,208,129,130,212,213,168,133,217,134,220,136,174,219, 224,139,227,140,229,150,142,232,234,144,145,187,239,241,149,244,240,151,194,247,154,250,155,252,254, 157,257,259,160,261,162,264,163,266,260,269,166,167,214,273,274,170,218,175,172,279,281,283,176,285, 286,178,289,180,230,291,183,233,184,235,288,295,297,188,192,189,301,263,191,305,306,195,303,309,197, 312,199,253,200,316,256,202,320,203,210,205,324,243,207,328,209,267,296,211,326,271,334,215,216,275, 339,277,342,221,280,222,346,223,349,225,226,353,236,228,357,231,360,361,362,237,268,238,302,368,369, 242,298,248,366,245,246,332,322,249,377,374,251,381,383,315,255,387,388,386,258,392,308,394,262,325, 270,391,265,343,399,401,307,403,272,405,407,409,338,276,340,413,278,329,416,418,282,421,393,284,424, 351,425,287,427,428,430,290,433,434,292,293,294,438,371,440,304,373,299,300,445,364,447,367,311,451, 453,310,455,456,458,313,459,314,461,385,319,317,318,467,468,327,321,348,323,471,472,397,475,330,464, 331,402,333,404,335,483,336,441,337,410,488,490,341,492,494,344,496,345,499,501,347,503,505,350,352, 506,354,355,510,356,512,432,358,359,517,515,446,363,519,365,408,442,522,525,370,437,372,474,529,531, 375,452,376,535,378,379,539,380,382,542,384,544,545,400,541,547,389,390,479,495,395,396,473,448,398, 555,557,559,469,480,561,563,406,566,568,569,571,411,573,412,491,414,578,415,470,417,582,583,419,500, 420,580,422,504,423,426,591,508,593,429,596,431,599,600,436,516,435,605,439,550,521,443,609,610,444, 613,614,528,449,618,450,620,621,623,454,626,537,628,457,631,465,460,606,462,463,546,466,581,634,520, 638,639,588,640,476,643,477,645,478,648,481,562,482,564,565,484,654,485,486,657,487,572,489,574,659, 663,665,493,668,502,548,497,498,619,674,633,677,553,679,681,507,684,509,604,683,511,688,689,513,514, 692,693,650,594,518,543,696,697,523,524,612,611,526,527,615,705,707,530,584,532,533,637,534,715,716, 536,719,538,722,718,540,632,586,549,729,730,622,551,552,554,736,642,556,739,558,646,738,560,660,603, 651,744,746,567,655,750,570,658,575,649,754,756,576,759,577,760,667,579,764,670,763,765,767,585,769, 771,587,774,589,776,590,779,595,592,781,782,784,597,598,786,788,601,602,694,791,607,608,795,699,796, 709,797,749,790,616,801,617,803,701,806,711,809,713,714,624,625,814,630,627,726,818,629,773,820,822, 720,727,810,635,636,828,829,830,831,833,641,761,647,644,740,811,837,743,652,841,653,843,844,703,656, 846,848,753,661,766,662,852,853,664,666,737,856,671,669,672,755,673,860,675,862,676,864,723,678,867, 680,800,870,682,873,685,686,876,687,877,690,879,691,789,704,695,883,875,794,698,700,702,888,799,777, 706,890,708,804,892,710,894,895,712,728,741,900,813,717,904,816,817,721,907,724,909,725,903,910,911, 826,912,731,732,733,734,915,735,918,920,922,742,838,839,863,745,925,747,748,929,751,847,752,932,850, 851,757,758,935,855,762,937,938,940,768,942,770,840,772,947,946,775,951,927,778,952,943,780,955,793, 783,785,878,787,958,960,953,792,941,962,964,887,798,967,802,969,805,972,807,808,902,968,898,975,812, 901,896,823,815,980,906,819,908,821,824,825,827,913,914,832,916,989,834,992,835,921,836,982,994,842, 996,869,998,845,966,999,849,933,970,854,1002,857,858,1003,859,884,861,872,1005,945,866,865,1009,997,1011, 868,871,882,1014,874,1017,957,880,1020,881,1016,885,963,886,1024,930,889,897,891,934,971,893,973,974,899, 1029,977,1031,1028,905,1034,923,1035,984,1026,1038,987,1039,917,990,1041,919,1027,924,1043,926,949,928,931,1047, 1049,936,939,1052,944,1006,1007,1008,948,1057,950,1059,1013,954,1055,961,956,1022,1065,959,1021,1018,1023,965,1068, 985,993,979,976,1073,978,1032,1033,981,983,1067,1077,986,988,1074,991,1042,995,1082,1081,1046,1000,1085,1001,1050, 1051,1004,1087,1071,1015,1086,1010,1058,1012,1089,1061,1062,1090,1069,1019,1092,1036,1025,1064,1094,1054,1072,1030,1040,1075, 1093,1037,1098,1079,1100,1045,1044,1101,1084,1048,1056,1053,1088,1060,1063,1091,1066,1076,1070,1107,1108,1097,1078,1099,1080, 1083,1111,1109,1104,1112,1106,1095,1096,1103,1110,1102,1105,1113,1114,1117,1116,1115,1118,1119,1120] ,\[ 2,4,5,7,8,9,1,12,14,15,16,3,18,19,21,23,24,26,6,27,28,29,30,31,32, 33,35,10,38,11,40,42,13,44,46,47,48,50,51,17,53,55,56,58,59,20,60,61,62,22, 64,65,67,68,25,69,70,72,74,76,78,80,81,83,84,85,86,88,89,91,92,34,93,95,96, 36,98,37,99,101,102,103,39,105,107,41,108,109,43,111,113,115,117,118,45,121,122,124,126,127, 49,129,130,131,52,133,134,136,54,138,139,140,57,142,144,145,147,149,150,151,153,154,155,157,158, 160,162,163,63,166,167,168,170,66,172,174,175,176,178,180,181,183,184,71,187,188,73,189,191,192, 194,195,75,197,199,200,77,202,203,79,205,207,209,210,211,82,214,215,216,218,219,221,222,87,223, 225,226,90,228,230,231,206,233,235,236,237,238,240,242,243,94,245,137,246,248,249,97,251,253,255, 256,258,212,260,262,263,100,265,267,268,270,271,272,104,229,275,276,106,277,278,280,282,193,284,110, 287,288,290,132,112,292,224,114,257,293,294,296,116,298,299,300,302,303,304,119,120,307,308,310,311, 313,314,123,315,317,318,319,125,321,322,323,325,326,327,329,330,128,331,332,333,159,335,336,337,338, 340,341,343,344,135,345,347,348,350,351,352,354,355,356,358,359,141,143,363,364,365,366,367,146,370, 291,148,371,372,373,374,375,152,376,378,379,380,382,384,385,386,156,389,390,391,387,393,395,396,161, 182,397,398,353,400,164,402,165,404,406,408,410,169,411,412,171,414,415,417,419,420,173,422,423,232, 383,426,208,177,429,431,432,179,435,436,403,437,185,439,186,441,442,443,444,446,190,448,449,450,452, 454,381,196,457,346,394,198,460,462,463,464,465,466,201,234,469,320,204,470,424,473,474,476,477,478, 427,479,480,481,482,213,484,485,486,487,489,217,491,493,220,495,497,498,500,312,502,504,440,261,430, 507,508,509,227,511,513,514,515,516,301,518,519,520,521,522,523,239,524,526,527,241,528,244,530,532, 533,247,534,536,537,538,250,540,541,285,543,252,254,546,259,548,549,550,392,377,551,552,553,264,554, 556,558,266,269,560,562,564,565,567,273,570,274,572,574,575,576,577,579,580,581,434,279,584,585,281, 586,587,588,283,589,590,286,592,594,595,597,598,289,601,602,603,604,606,607,608,295,349,297,611,612, 593,615,616,617,305,619,306,622,624,625,309,627,629,630,632,503,610,582,633,634,316,453,635,636,637, 563,609,324,641,642,328,644,646,647,361,649,334,650,651,652,653,599,655,656,658,659,660,661,339,662, 664,666,667,342,669,670,671,672,673,675,676,678,459,680,682,683,401,369,685,686,687,425,690,407,691, 357,694,496,555,695,360,362,698,699,700,368,701,702,703,704,706,708,709,710,711,712,713,714,547,717, 718,720,721,723,724,725,726,727,728,388,731,732,733,734,735,737,517,738,740,741,399,742,743,744,471, 405,745,747,748,749,751,752,409,628,753,755,757,758,413,525,761,762,763,688,416,461,766,418,768,770, 772,773,421,775,777,778,692,780,679,428,783,785,494,542,787,789,506,790,433,792,793,794,438,472,689, 665,798,799,445,800,447,802,804,805,807,808,810,451,811,812,813,815,816,817,455,571,819,456,821,823, 458,824,825,826,827,467,468,705,832,834,657,475,835,836,829,837,838,839,840,483,842,801,739,845,693, 847,849,488,626,850,851,490,854,855,750,492,857,786,858,716,859,631,759,861,499,863,501,865,866,868, 869,505,871,872,874,875,769,510,803,856,878,512,880,881,760,882,884,885,886,614,844,887,889,795,638, 566,730,891,529,893,870,531,896,897,898,899,901,902,903,535,754,905,906,908,904,539,909,767,544,545, 852,707,900,557,913,914,916,917,919,921,654,923,559,924,561,830,926,927,928,568,930,569,931,736,573, 822,933,934,936,674,596,578,939,583,941,943,944,945,946,948,949,950,684,918,935,953,954,746,591,956, 797,957,668,937,959,600,961,853,605,963,965,966,722,613,968,970,971,618,947,973,620,974,621,623,976, 977,765,978,979,981,982,983,888,756,791,984,985,986,987,988,639,990,991,640,993,643,955,645,648,995, 873,997,967,831,860,960,1000,729,938,1001,663,892,883,1004,1005,846,788,782,1006,1007,989,1008,677,1010,1012, 1013,1003,681,1015,1016,992,1018,1019,942,1021,910,1022,696,1023,697,876,796,1025,952,784,879,1026,1027,1024,1028, 1030,715,1032,1033,932,719,998,1036,1029,1037,841,929,994,1038,1040,776,781,1020,1042,1044,1014,1045,818,1046,1048, 806,1050,1051,764,1053,1054,771,1055,1056,774,1058,1060,1035,1061,779,1062,1063,1064,964,1066,848,1067,958,809,1069, 1011,1070,1071,1072,828,1074,814,820,1075,1076,1057,1078,864,1079,833,1080,915,1081,1083,843,1084,1049,980,1031,1052, 969,1086,1088,862,894,1085,907,972,996,867,1059,922,1089,877,1091,920,1082,1093,890,895,1092,911,1095,1047,1096, 951,1097,912,1099,1101,1102,962,925,1103,1104,1002,1105,940,1100,1043,1098,975,1077,1106,1094,1109,1068,1107,1110,1017, 1111,1090,999,1009,1113,1073,1065,1114,1034,1039,1041,1115,1116,1112,1108,1087,1118,1119,1120,1117] >; print "Group G is S6(3):2 < Sym(1120)";