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