/* www-ATLAS of Group Representations. 3.G2(3) represented as permutations on 1134 points. */ G:=PermutationGroup<1134|\[ 306,761,628,790,173,933,643,451,690,10,578,368,160,370,158,871,887,543,652,60,1133,484,792,821,118, 658,977,45,826,274,948,1120,377,548,35,699,837,988,1084,926,303,824,603,895,28,126,205,48,479,124, 903,76,73,524,590,216,456,475,592,20,606,390,816,139,817,841,794,1123,69,364,505,1087,53,1048,386, 52,831,230,455,904,326,741,1067,558,342,540,946,896,248,90,883,651,250,290,249,708,188,362,612,769, 806,746,343,715,649,133,195,549,1128,742,111,872,911,114,363,482,329,25,359,915,539,358,152,50,1012, 46,698,1010,292,495,781,979,106,266,317,637,607,283,64,547,960,371,1081,304,297,586,1061,148,797,566, 728,123,630,804,886,533,546,15,839,13,278,740,986,597,372,253,793,560,323,927,610,172,5,964,1101, 583,318,424,696,217,1064,291,494,373,615,730,914,97,828,308,867,497,466,1054,107,751,489,305,199,1082, 426,231,203,459,47,616,710,638,786,210,731,922,814,1038,244,56,180,321,621,855,918,276,675,732,984, 307,450,924,834,78,202,582,452,1018,261,925,574,618,293,1125,1016,242,243,215,286,561,600,89,95,93, 760,966,166,878,449,993,257,437,856,311,235,262,801,1083,996,134,770,685,799,577,976,563,692,30,393, 222,991,161,654,519,503,1089,138,346,748,245,943,858,598,94,182,129,239,412,727,1129,145,1056,680,863, 1045,623,41,144,198,1,226,190,485,992,260,989,973,703,1026,552,135,177,516,994,218,1112,169,408,686, 81,504,1121,117,838,877,735,620,415,909,679,723,668,445,341,340,85,103,522,667,284,712,663,423,526, 880,413,487,537,640,750,520,122,119,1011,403,98,115,70,764,910,472,12,1115,14,142,165,184,457,534, 842,33,1004,379,949,851,953,864,1092,588,75,1104,913,1053,62,502,480,275,811,1127,471,464,942,481,634, 743,1051,361,1059,762,836,492,324,941,724,753,294,352,655,334,430,768,726,672,420,422,421,349,178,596, 201,573,788,765,416,431,773,1057,705,470,530,258,1088,789,488,975,674,968,843,339,1015,521,857,255,227, 8,233,866,898,79,57,374,1085,204,906,518,937,815,397,609,193,511,1111,662,435,396,367,709,602,58, 755,683,673,49,392,399,116,958,22,309,545,353,440,197,978,1052,407,1102,183,130,1124,192,498,632,500, 829,391,281,327,71,625,930,700,656,955,467,1117,954,1079,897,319,738,461,280,357,447,344,523,54,624, 350,936,1058,1100,436,1034,532,156,375,1126,985,354,1105,121,86,1033,737,18,882,486,157,140,34,108,983, 1022,316,1040,846,756,556,853,84,947,168,246,928,272,1046,1078,150,881,859,938,1113,798,905,427,237,579, 970,270,11,575,580,678,232,176,584,639,146,1063,385,1095,55,684,59,1098,759,1062,425,164,289,736,247, 766,474,43,1001,1041,61,137,1116,465,171,611,99,647,1090,185,206,665,238,899,333,219,653,302,525,506, 1134,661,3,763,153,934,499,1027,400,998,1039,136,208,585,355,1007,812,7,644,796,657,613,1050,105,664, 92,19,622,279,414,509,646,26,691,785,627,469,348,650,617,1036,345,338,1025,695,707,419,478,442,223, 1000,852,581,336,299,875,1070,477,591,268,325,713,894,807,9,659,273,778,827,670,179,961,127,36,508, 813,892,314,1029,434,729,671,96,473,207,840,347,687,1008,104,1103,912,718,874,720,721,745,337,410,1049, 418,295,151,706,186,211,224,733,734,332,599,542,517,1069,162,82,110,401,744,722,102,754,285,803,356, 196,1075,411,747,476,555,1047,907,594,251,2,405,629,365,429,601,850,417,100,267,1107,873,432,774,919, 835,980,693,1020,916,131,805,1131,982,660,209,787,428,439,4,844,23,167,67,1003,645,149,571,269,800, 263,917,749,154,782,101,689,1023,845,825,394,642,701,213,463,63,65,995,990,884,24,987,1013,42,810, 29,694,189,501,876,77,969,833,229,776,406,37,330,159,711,66,376,444,791,809,554,1035,1065,963,767, 381,677,557,1024,220,259,448,288,568,860,997,1042,300,383,865,453,191,868,869,931,16,112,772,719,681, 830,331,254,999,351,567,544,91,820,1060,155,17,1109,1076,951,900,702,893,688,44,88,515,454,619,891, 923,1093,51,80,572,460,758,908,335,366,113,717,388,187,120,780,802,221,775,920,1014,212,901,228,236, 40,170,562,929,507,870,1017,6,631,939,527,462,569,935,1037,409,398,287,1118,1122,87,559,31,380,950, 890,1043,382,513,510,1077,1044,483,1073,141,697,965,849,174,962,252,1072,443,832,576,1132,1055,313,1106,441, 271,27,490,132,777,1091,784,550,225,536,163,822,38,312,819,277,310,256,320,818,265,861,635,879,676, 604,1119,795,378,1019,1108,641,714,1009,128,360,125,823,921,446,241,932,234,1005,779,1021,551,808,854,669, 315,633,1074,704,1030,1066,1080,541,531,847,666,940,214,636,553,605,862,952,957,301,564,757,74,725,648, 402,491,389,194,972,298,433,528,404,885,147,595,587,181,848,1031,83,1130,739,682,1071,967,959,1028,752, 889,956,565,514,1032,143,200,264,39,458,1094,72,438,282,614,981,384,902,1086,589,1099,1097,593,1096,529, 175,493,716,387,538,974,771,1006,888,1110,468,322,570,1114,369,608,512,944,1002,32,328,945,68,496,240, 535,395,109,296,1068,783,971,21,626] ,\[ 540,557,21,483,167,1061,531,307,454,874,942,853,367,573,419,250,96,377,867,849,1073,586,133,501,811, 455,422,281,266,552,339,1033,829,537,294,505,1050,434,825,437,370,34,608,609,739,576,972,391,522,682, 80,1083,790,893,1112,695,382,456,1004,433,989,1068,1047,743,283,397,681,84,737,841,44,78,1098,896,528, 780,719,306,625,485,964,1058,353,449,141,520,539,658,945,1110,417,526,151,62,1117,176,547,61,774,736, 368,1121,559,19,269,638,136,291,560,795,38,969,888,384,228,467,663,937,742,1097,670,448,846,683,352, 414,190,452,206,69,196,987,326,412,120,380,47,762,329,886,611,974,857,103,100,910,1049,1114,1092,633, 918,1013,308,316,148,18,87,809,684,226,1074,1014,194,543,182,1046,721,362,399,134,97,106,636,726,251, 17,803,153,949,443,118,490,302,400,626,423,1040,6,95,284,358,933,508,1101,482,968,388,868,1009,1072, 583,332,847,54,125,621,351,225,794,1003,773,224,435,880,14,177,138,620,446,720,7,707,850,381,582, 760,614,472,37,667,786,578,333,511,924,662,1024,43,603,855,143,371,735,1057,175,1130,300,1078,49,430, 245,666,875,645,9,1082,428,1060,898,1028,1089,643,407,729,525,535,550,76,799,655,530,325,409,660,453, 1128,187,8,598,692,615,64,807,127,264,392,820,420,26,812,1125,613,650,651,596,259,1106,73,1122,523, 1077,669,263,994,184,72,278,178,1127,653,113,865,671,222,200,1091,551,159,180,600,830,478,1039,445,570, 23,152,599,904,998,585,915,877,1042,826,89,529,939,1102,770,754,425,436,930,999,728,1029,257,57,975, 1096,205,383,581,295,859,796,950,378,56,1055,961,1001,946,843,24,1123,821,1120,460,723,959,685,882,734, 906,156,480,977,107,212,349,83,1011,701,659,374,899,451,77,618,958,432,674,686,411,932,312,595,305, 779,536,288,907,814,630,303,577,986,815,544,170,1133,632,484,828,441,694,617,403,487,1059,624,365,1109, 627,121,348,691,16,757,1023,827,111,1043,1036,839,81,936,634,91,641,319,174,1006,816,1027,824,68,1035, 920,1100,938,255,289,891,179,195,495,41,840,86,211,109,372,509,1063,702,1118,149,112,115,234,955,1015, 261,99,1087,331,359,1,458,1056,740,51,781,798,232,356,165,236,558,833,901,976,67,271,677,885,158, 366,792,394,173,894,79,801,777,1020,474,473,354,401,616,426,244,214,745,724,462,1030,249,247,320,758, 665,604,549,566,497,221,402,842,1065,29,532,42,1104,157,481,856,237,988,396,227,705,171,876,75,631, 1115,793,1012,447,782,710,954,791,144,464,287,1070,943,555,709,337,209,912,345,272,439,124,215,628,800, 732,908,488,235,768,512,208,966,562,479,834,274,725,198,805,429,292,185,1071,169,355,386,746,808,524, 499,253,963,759,911,697,848,238,71,418,85,223,592,545,28,1086,15,48,605,1119,129,1103,53,186,506, 593,515,1005,864,967,267,126,873,664,704,504,649,172,344,622,1021,997,971,982,970,755,280,33,700,941, 35,270,764,979,652,749,1032,712,597,587,74,491,1002,440,92,751,881,50,183,427,902,276,90,503,11, 538,1022,788,698,708,496,668,572,318,822,787,771,1113,475,357,591,647,431,610,360,1076,928,1026,835,637, 965,838,926,1067,1008,10,314,718,817,802,818,88,590,290,321,299,110,680,390,804,5,12,242,866,1129, 444,917,772,285,1093,957,46,533,810,750,145,130,246,863,415,55,878,282,871,1054,279,59,1031,1132,243, 252,256,851,921,858,369,693,265,527,160,301,217,696,310,654,870,469,1111,744,897,1084,346,463,477,405, 502,193,688,513,268,947,564,39,364,541,813,395,832,258,623,492,776,30,567,717,690,629,421,105,922, 1064,556,216,220,713,534,65,328,500,375,919,714,231,775,1107,219,565,1090,703,561,101,373,240,122,783, 927,60,1116,648,715,1025,678,1081,22,978,1053,892,468,40,983,845,733,424,82,70,1034,992,862,900,612, 991,260,722,494,823,785,241,646,489,553,52,607,45,797,398,519,104,589,766,869,769,903,150,706,602, 1126,233,119,1131,517,230,387,642,914,601,1018,450,311,521,248,58,1007,204,36,323,661,340,296,197,20, 854,313,984,139,1066,923,1017,408,644,1041,619,973,727,1124,202,1080,913,93,25,389,341,575,376,579,948, 819,335,606,297,639,1075,66,980,199,309,571,181,275,1079,657,293,675,951,831,336,784,486,1108,457,191, 563,350,730,2,510,594,1048,286,465,132,168,32,239,438,385,201,406,131,471,254,262,137,568,1044,952, 459,990,699,765,192,147,909,461,872,879,273,960,164,98,379,753,203,210,1085,102,161,883,1062,569,162, 1016,117,993,747,574,324,837,546,934,63,114,860,327,1000,689,363,404,140,361,466,442,498,393,542,944, 679,554,852,1099,889,1134,940,962,123,887,343,166,1095,895,277,146,1051,213,142,836,1037,1010,731,981,229, 334,905,1045,518,1019,4,516,844,27,789,188,330,116,507,806,1052,635,94,413,584,956,315,3,996,1105, 763,761,890,338,1088,493,752,861,687,304,514,322,916,476,711,154,470,953,1038,1094,207,135,298,347,128, 163,31,640,676,931,929,410,925,342,673,580,741,778,155,317,416,189,767,218,756,995,716,13,884,108, 548,935,672,588,738,985,656,1069,748] >; print "Group G is 3.G2(3) < Sym(1134)";