/* www-ATLAS of Group Representations. O7(3) represented as permutations on 1120 points. */ G:=PermutationGroup<1120|\[ 2,1,4,3,7,9,5,12,6,15,17,8,20,22,10,24,11,27,29,13,32,14,33,16,36, 38,18,41,19,44,46,21,23,50,52,25,55,26,58,60,28,63,65,30,68,31,70,71,73,34, 76,35,79,81,37,84,85,39,88,40,91,93,42,96,43,99,100,45,103,47,48,107,49,110,112, 51,115,117,53,120,54,123,125,56,57,128,130,59,133,135,61,138,62,141,143,64,146,147,66,67, 151,121,69,155,157,159,72,124,163,74,166,75,169,171,77,174,78,176,178,80,102,180,82,108,83, 185,187,86,190,87,193,194,89,197,90,200,202,92,205,207,94,181,95,212,213,97,98,216,218,167, 101,222,224,226,104,177,105,231,106,208,235,210,109,239,240,111,150,244,113,245,114,249,251,116,254, 118,156,119,259,122,142,262,247,265,126,250,127,269,271,129,274,276,131,132,280,282,134,284,285,136, 288,137,291,290,139,295,140,160,299,162,302,144,145,253,307,148,310,149,313,277,316,152,319,153,303, 154,323,325,327,329,158,332,334,298,161,338,340,342,164,165,346,348,350,168,170,353,183,356,172,186, 173,360,214,175,364,366,368,370,179,373,352,182,377,379,184,382,371,385,188,388,189,391,390,191,395, 192,220,399,401,195,402,196,394,198,199,408,410,201,413,204,203,417,411,420,206,423,424,234,209,428, 430,211,225,406,435,436,215,439,441,217,444,446,219,449,451,221,453,455,223,458,460,462,227,464,228, 466,229,469,230,447,473,232,476,233,478,480,482,236,485,237,488,238,359,491,493,241,496,242,492,243, 501,261,246,503,505,248,508,497,343,252,499,513,515,255,516,256,519,257,521,258,267,500,260,527,529, 531,263,533,264,535,536,266,524,540,268,543,545,270,547,273,272,551,553,283,275,557,558,539,278,561, 279,281,565,567,568,304,571,286,573,287,293,577,289,481,581,583,292,586,588,294,590,589,296,297,594, 596,598,300,600,301,603,541,564,606,305,306,591,611,308,614,309,615,587,311,619,312,330,622,314,494, 315,514,317,627,318,459,630,320,456,321,592,322,635,324,638,326,641,642,328,644,612,538,331,580,625, 333,649,335,651,336,414,337,655,654,339,658,659,341,662,664,344,349,345,450,669,347,358,672,361,372, 351,676,354,677,355,679,537,357,668,608,520,673,362,452,363,365,688,689,367,511,369,692,671,383,674, 696,374,697,375,701,376,704,378,706,380,381,507,472,398,384,432,712,386,714,387,716,389,718,719,665, 392,723,393,726,710,728,396,397,731,732,400,734,736,433,403,684,404,405,727,742,407,744,409,652,748, 597,412,749,751,474,415,754,416,756,753,418,443,419,422,421,437,461,729,425,764,426,576,427,767,429, 768,771,431,774,775,434,777,510,779,702,438,471,783,440,442,786,788,785,445,791,781,448,793,794,475, 738,454,796,799,457,801,647,711,722,463,805,807,465,810,811,467,468,814,470,816,773,632,720,477,820, 479,574,823,484,483,826,827,486,487,802,815,489,833,490,550,836,838,509,495,839,523,498,512,525,842, 502,504,844,506,845,847,691,849,566,757,853,855,517,518,858,682,522,854,862,860,526,528,865,866,867, 530,610,822,532,871,534,874,861,876,555,633,542,879,544,881,546,883,548,549,648,885,634,552,888,890, 554,569,556,593,894,559,560,787,562,900,563,903,626,905,907,909,570,782,572,821,911,913,575,578,915, 579,917,585,582,765,584,685,921,891,923,916,918,831,595,755,914,599,601,930,931,602,784,646,604,605, 935,607,936,609,939,621,743,613,772,618,616,733,617,945,946,620,846,623,624,798,628,837,795,629,951, 631,660,812,848,636,955,637,957,958,639,640,803,834,643,661,645,877,963,960,650,745,703,653,965,870, 656,657,968,884,966,763,971,663,813,975,666,797,667,670,979,873,675,981,678,680,792,681,804,683,985, 950,984,686,693,687,972,926,690,992,695,708,694,956,996,698,699,700,901,999,825,705,1001,841,707,998, 709,817,1005,713,1007,715,1009,717,829,721,1010,1011,724,1002,725,759,994,1014,730,1016,969,983,1019,934,735, 868,1015,737,976,739,1022,740,1024,741,1027,746,1029,747,766,750,761,752,762,1025,1032,758,932,760,974,1030, 857,1034,1039,1040,769,770,922,1038,899,776,778,1045,1046,780,1049,952,1050,1000,947,789,790,944,1053,1004,851, 800,941,987,1056,806,863,808,809,1057,819,1017,1059,818,1060,824,830,1063,828,896,1064,832,856,1066,924,835, 904,1068,1052,840,1069,843,997,897,852,850,1073,953,1003,1026,1076,1078,859,1077,892,1070,864,982,875,869,943, 872,889,988,949,878,1082,880,1083,882,886,887,1013,1012,893,902,895,961,1072,898,1067,1054,906,1084,908,919, 989,910,1090,912,925,1092,920,1037,927,1094,1096,1033,933,928,929,1079,1062,1098,1081,937,938,1099,1101,940,942, 1102,978,948,1021,1104,954,959,1095,962,964,1071,1042,967,970,1080,973,1020,977,980,995,1061,1018,986,1093,1089, 990,993,991,1041,1065,1044,1006,1008,1023,1086,1085,1113,1107,1075,1028,1114,1031,1074,1035,1058,1036,1103,1043,1047,1108, 1048,1051,1097,1055,1115,1112,1088,1100,1111,1119,1109,1106,1087,1091,1105,1117,1116,1120,1110,1118] ,\[ 3,1,5,6,8,10,11,13,14,16,18,19,21,23,24,25,26,28,30,31,2,33,34,35,37, 39,40,42,43,45,47,48,49,51,53,54,56,57,59,61,62,64,66,67,63,69,68,72,74,75, 77,78,80,82,83,4,86,87,89,90,92,94,95,97,98,88,101,102,104,105,106,108,109,111,113, 114,116,118,119,121,122,124,126,71,127,129,131,132,134,136,137,139,140,142,144,145,7,148,149,150, 152,153,154,156,158,160,161,162,164,165,167,168,170,172,173,9,175,177,178,93,179,181,182,183,184, 186,188,189,191,192,147,195,196,198,199,201,203,204,206,208,209,210,211,12,185,214,215,217,219,220, 221,223,225,227,228,229,230,232,233,234,236,237,238,103,241,242,243,245,246,247,248,250,252,253,255, 256,257,258,15,260,261,263,264,266,240,267,268,270,272,273,275,277,278,279,281,110,283,17,286,287, 289,290,292,293,294,296,297,298,300,301,303,304,305,306,308,309,311,312,314,315,317,318,320,321,20, 322,324,326,328,330,331,333,335,336,337,339,341,343,344,345,347,349,22,351,352,354,355,357,166,358, 359,361,362,363,365,367,369,371,372,374,375,376,378,380,381,383,384,386,387,389,390,392,393,394,396, 397,398,400,402,403,29,404,405,406,407,409,411,412,414,415,416,418,419,421,422,27,425,426,427,429, 431,432,433,434,194,437,438,440,442,443,445,447,448,450,452,213,454,456,457,459,461,463,464,73,465, 467,468,470,471,472,474,475,477,478,479,481,483,484,486,487,32,489,490,492,494,495,497,498,499,500, 502,417,408,504,506,507,509,510,444,511,512,514,356,327,517,518,323,520,522,523,524,525,526,528,530, 532,505,534,535,36,537,538,539,541,542,544,546,216,548,549,550,552,554,555,556,38,557,559,560,562, 563,564,566,313,569,570,572,573,574,575,576,578,579,580,582,584,585,587,493,589,591,592,593,594,595, 597,529,599,601,602,41,604,605,607,608,609,610,612,613,58,282,616,617,618,620,621,540,623,624,625, 626,469,85,310,628,629,631,632,44,633,634,635,636,637,639,640,332,551,643,46,342,645,125,646,647, 648,650,651,652,653,84,654,656,603,657,649,660,661,663,665,666,521,667,668,670,671,133,615,673,674, 675,295,677,678,679,50,547,476,680,681,682,683,684,685,686,687,395,364,690,691,692,52,693,694,695, 697,698,699,700,702,703,705,706,707,708,709,307,710,711,460,55,713,285,715,123,717,561,453,720,721, 722,724,725,346,727,117,729,730,641,733,669,735,737,316,738,739,740,741,619,743,744,745,746,747,749, 370,658,750,752,60,753,401,755,269,757,664,758,759,731,760,761,762,763,480,765,766,120,583,768,769, 770,772,773,732,776,193,778,688,780,774,781,782,784,627,785,787,151,789,790,65,536,792,794,795,796, 797,798,399,775,800,777,802,803,325,804,806,808,809,224,449,812,813,100,815,817,818,155,819,783,70, 821,822,824,825,701,816,828,829,226,830,831,832,553,834,835,837,716,96,254,190,840,197,841,805,413, 843,844,764,807,846,76,848,850,851,852,854,856,284,857,859,860,861,200,79,410,863,864,754,793,868, 869,81,870,866,872,873,545,875,611,877,473,878,880,598,882,138,291,146,884,622,886,366,887,889,329, 891,786,892,893,895,896,897,898,899,901,902,202,904,906,908,910,239,435,911,600,912,914,827,259,916, 439,918,642,919,515,920,112,91,922,894,903,244,924,925,926,927,928,929,543,932,159,933,934,718,791, 936,937,845,938,940,941,265,107,942,943,944,888,348,905,672,799,947,838,441,948,99,949,950,222,952, 276,953,218,954,696,956,921,176,959,915,960,130,961,157,962,909,814,862,935,491,964,771,187,966,662, 568,967,385,969,712,970,972,973,974,976,977,644,180,978,373,249,980,590,596,982,983,984,531,689,115, 986,987,988,714,989,990,991,992,874,993,742,994,995,496,586,997,436,998,779,360,1000,855,853,1002,1003, 917,1004,1006,482,485,1008,823,205,811,833,957,638,388,128,1012,319,1013,958,1015,1005,1017,1018,931,939,513, 606,1020,883,567,1021,1023,885,1025,1026,1028,430,1030,588,135,999,1016,723,1031,736,1033,1034,1035,728,1036,169, 1037,1038,516,1041,1042,455,141,571,1043,1044,143,726,1047,1048,881,446,1051,1010,1052,1053,836,271,1022,1045,1054, 382,907,1055,748,865,659,839,801,876,946,1058,820,451,930,1061,1062,462,1032,1064,1065,1027,879,630,1067,1068, 163,719,391,299,1070,423,212,171,1071,1072,1074,174,1075,262,1077,1063,849,1060,231,350,734,1079,979,923,971, 847,965,1080,1081,842,340,655,867,751,788,1084,1085,810,1086,1087,1076,1050,1040,1088,527,251,466,1024,280,565, 235,1089,1091,756,1092,501,1093,1094,1095,1096,1097,207,503,368,302,1098,334,1099,1057,1100,1101,1007,1102,428,1103, 1009,274,1073,1104,1014,581,508,1056,614,1039,519,424,858,1090,1105,1106,955,1066,488,558,985,1107,1078,1108,1109, 288,767,1110,1046,1111,951,1029,826,975,1112,458,676,945,1114,1115,1083,353,890,1113,377,1116,981,1049,338,963, 1117,1118,420,1059,1069,1119,1001,900,533,1019,379,968,1082,1120,577,913,704,996,1011,871] >; print "Group G is O7(3) < Sym(1120)";