/* www-ATLAS of Group Representations. S4(7) represented as permutations on 1176 points. */ G:=PermutationGroup<1176|\[ 1,2,3,5,4,8,7,6,11,13,9,15,10,18,12,21,22,14,25,26,16,17,30,32,19, 20,36,38,29,23,42,24,33,46,35,27,50,28,53,55,57,31,60,61,63,34,66,48,69,37, 72,52,39,75,40,56,41,77,79,43,44,62,45,85,86,47,89,90,49,93,95,51,98,74,54, 76,58,103,59,105,107,109,111,113,64,65,87,118,67,68,121,122,70,94,71,127,129,73,132,134, 136,138,78,141,80,143,81,146,82,110,83,150,84,114,119,154,156,88,115,160,91,92,164,166,168, 169,96,172,97,175,177,99,180,100,182,101,184,102,187,189,104,192,106,195,145,108,198,199,201,112, 203,205,207,116,209,117,212,158,159,120,216,218,220,123,165,124,225,125,126,229,231,128,234,174,130, 176,131,183,238,133,241,135,178,137,245,186,139,248,140,251,253,142,193,257,144,260,262,147,148,200, 149,202,151,267,152,270,153,208,155,273,275,157,215,279,213,161,282,162,285,163,287,289,223,224,167, 226,293,228,170,297,171,232,301,173,304,306,308,179,239,274,181,313,315,317,185,246,321,188,324,250, 190,327,191,330,332,333,194,336,259,196,261,197,342,344,346,266,204,348,350,206,353,355,210,240,211, 358,307,361,214,364,331,217,368,309,219,286,221,370,222,373,374,376,227,378,380,381,230,384,385,300, 233,302,390,235,393,236,277,237,284,399,400,312,242,402,243,316,244,405,404,407,247,410,389,249,414, 416,252,419,420,254,281,255,256,425,426,258,429,431,433,365,434,263,343,264,439,265,441,268,444,269, 351,447,271,450,272,452,357,276,455,457,278,459,460,280,340,462,464,283,445,288,469,470,290,291,473, 292,377,294,478,295,296,480,383,298,299,485,487,488,323,303,401,392,305,394,395,403,494,496,310,311, 391,314,396,319,318,505,320,408,507,322,510,512,514,325,516,326,519,521,328,329,525,527,529,531,334, 335,534,535,337,538,338,524,339,341,541,543,545,546,345,549,347,551,553,349,369,557,352,560,562,354, 565,356,567,569,359,571,360,540,362,363,573,366,520,367,465,466,578,580,371,372,576,472,375,586,475, 588,477,379,568,382,594,596,598,600,386,603,387,388,489,608,609,611,613,397,615,398,617,498,620,622, 623,624,625,626,406,629,409,508,509,411,632,412,634,413,636,415,638,639,417,463,418,644,646,432,421, 649,422,528,423,651,424,653,614,427,428,536,657,430,660,458,435,548,436,665,437,438,668,542,440,556, 442,672,443,675,677,550,446,681,682,448,685,449,687,689,451,692,453,479,454,695,456,697,461,699,680, 471,577,467,702,468,703,705,707,584,710,474,592,476,713,715,717,587,696,481,720,482,721,483,724,484, 601,602,486,729,730,631,725,490,491,610,492,734,493,533,495,737,497,738,652,499,740,500,501,502,503, 504,745,747,506,630,606,511,752,513,755,515,733,517,518,750,759,700,761,522,645,523,765,648,526,768, 530,619,532,771,655,718,537,706,659,539,777,779,663,781,544,783,785,547,669,789,791,552,691,674,554, 676,555,795,679,575,558,559,798,800,561,803,563,806,564,690,673,566,809,727,570,593,572,813,574,642, 701,579,581,704,582,658,583,820,799,585,823,825,589,828,590,716,591,656,787,595,597,833,834,599,607, 837,694,804,604,605,731,842,637,612,844,845,616,618,739,621,847,742,743,849,627,851,628,853,749,640, 855,633,858,860,635,756,757,864,641,867,643,870,871,764,647,766,874,650,877,770,654,878,782,880,882, 776,661,778,662,884,664,773,666,887,667,868,719,890,670,859,671,894,895,897,678,899,900,683,709,684, 904,905,686,728,811,688,875,908,693,810,805,812,698,912,815,915,817,918,920,708,923,924,711,857,712, 848,827,714,930,931,933,935,722,723,835,907,726,846,839,840,841,732,843,735,736,838,741,826,744,947, 746,852,748,949,751,952,824,753,790,754,861,865,959,758,862,866,760,786,869,762,763,891,964,767,807, 914,769,772,968,774,970,775,913,780,974,976,784,978,889,788,872,982,983,792,793,986,794,989,796,797, 993,995,903,801,802,906,836,808,997,999,911,814,883,876,816,1003,917,818,1005,819,936,1008,821,822,1011, 991,1001,928,941,829,830,1014,831,1015,832,921,937,1017,1019,1020,929,1013,1022,1024,950,946,850,981,854,945, 951,856,953,961,1027,1028,972,958,863,960,954,1031,1032,873,965,1034,967,879,969,881,971,957,973,885,1040, 886,1042,888,1045,1038,948,892,893,1051,1053,896,1056,1058,898,990,926,1062,901,1007,902,996,909,1068,910,1070, 927,1071,916,1074,919,1006,994,922,1018,1075,925,1012,942,932,934,1081,938,1009,939,940,1085,943,1086,944,1025, 1026,955,956,1048,1087,962,963,1035,966,1033,1091,1093,980,1095,975,1097,977,1043,1099,979,1101,1088,1029,1049,1103, 984,1052,985,1072,1108,987,1111,988,1112,1060,1115,992,1117,1119,1120,1066,1077,998,1121,1000,1002,1054,1127,1004,1010, 1076,1067,1078,1092,1132,1016,1130,1083,1084,1021,1023,1030,1047,1113,1137,1036,1079,1037,1094,1039,1098,1041,1096,1044,1141, 1046,1107,1050,1140,1146,1106,1102,1055,1149,1145,1057,1059,1089,1114,1061,1116,1063,1150,1064,1065,1069,1155,1123,1124,1125, 1126,1073,1128,1153,1082,1159,1080,1133,1139,1135,1163,1090,1165,1134,1104,1100,1142,1143,1144,1110,1105,1168,1151,1109,1118, 1148,1171,1129,1172,1122,1156,1157,1158,1131,1160,1167,1162,1136,1164,1138,1166,1161,1147,1169,1170,1152,1154,1173,1174,1175, 1176] ,\[ 2,3,4,6,7,1,9,10,12,14,8,16,17,19,20,5,23,24,11,27,28,29,31,33,34, 35,37,39,40,41,43,44,45,47,48,49,51,52,54,56,58,59,13,62,64,65,67,68,70,71, 15,73,74,55,21,76,75,78,80,81,82,83,84,18,87,88,90,91,92,94,96,97,99,100,101, 22,102,104,61,106,108,110,112,114,115,116,117,119,120,25,26,123,124,125,126,128,130,131,133,135, 137,139,140,30,142,144,145,147,148,149,141,32,151,152,153,155,157,158,159,161,162,163,165,167,36, 170,171,173,174,176,178,179,38,181,183,175,185,186,188,190,191,193,194,42,196,197,199,200,79,202, 204,206,154,208,210,211,46,213,214,215,217,219,221,222,223,224,226,227,228,230,232,233,50,235,236, 177,72,237,239,240,242,243,53,244,57,246,247,249,250,252,254,255,256,258,259,261,263,264,60,218, 98,265,266,268,269,63,271,85,272,274,276,277,278,66,280,281,283,284,220,286,288,290,69,164,291, 292,294,295,296,298,299,300,302,303,305,307,201,309,310,311,312,314,316,318,319,320,322,323,77,325, 326,328,329,331,279,334,335,337,338,339,340,341,343,345,203,150,347,349,351,352,354,356,357,86,132, 359,360,362,363,365,366,367,89,109,369,121,207,371,372,166,375,93,377,379,273,382,383,95,386,387, 388,389,391,392,394,395,396,397,398,275,241,180,401,317,403,404,134,333,406,408,409,411,412,413,415, 417,418,103,421,422,111,423,424,105,427,428,430,432,419,107,435,436,437,438,440,160,442,443,113,445, 446,448,449,451,285,453,169,454,456,458,332,118,461,212,346,463,465,466,467,468,122,471,447,472,474, 475,476,477,380,168,479,481,482,483,484,486,127,489,490,491,304,234,492,129,493,136,495,497,498,499, 500,501,502,503,504,506,245,138,508,509,511,513,426,515,517,518,520,522,523,524,526,528,530,184,532, 533,480,536,537,143,539,433,195,540,542,544,146,547,548,550,260,552,554,555,556,558,559,561,563,564, 287,566,568,315,570,156,572,364,545,270,192,574,575,350,576,577,579,581,582,496,583,584,585,587,567, 589,590,591,592,593,595,597,599,601,602,604,605,606,607,172,610,612,614,494,616,368,618,619,621,535, 336,358,182,627,628,407,629,630,507,631,187,633,635,420,637,632,189,640,641,642,643,645,441,647,648, 650,434,644,308,546,652,654,636,655,656,402,658,659,661,662,663,664,353,666,667,361,669,670,671,198, 649,673,674,676,678,679,680,205,683,684,460,686,688,690,691,693,694,209,685,478,696,698,399,700,216, 701,470,444,355,596,704,706,708,709,711,712,225,376,714,716,718,657,257,719,229,485,722,723,725,726, 727,728,720,231,416,731,732,414,733,505,400,735,393,736,625,529,469,238,739,695,741,742,697,743,744, 622,746,390,748,749,750,751,753,754,248,324,756,757,758,487,760,251,646,762,763,764,766,755,767,253, 431,769,770,772,773,313,771,774,775,776,778,780,768,262,782,784,786,787,788,790,792,793,267,450,594, 794,785,796,464,797,370,703,799,801,802,804,805,543,781,553,807,808,810,588,562,811,812,814,815,816, 282,817,818,681,819,715,549,289,821,822,824,826,827,293,617,829,560,455,830,831,832,297,835,836,837, 713,838,580,839,840,841,301,615,843,613,306,844,828,573,846,611,848,571,609,850,806,852,410,321,854, 856,857,859,861,862,608,863,865,866,868,869,330,327,872,873,514,875,876,849,687,381,845,879,881,660, 538,883,651,882,527,885,765,886,342,888,803,889,344,891,892,893,880,896,348,898,578,901,902,373,903, 813,747,459,620,906,405,907,909,910,911,624,878,717,913,914,916,917,919,921,922,374,925,926,842,927, 905,928,929,378,932,934,936,937,759,938,939,384,385,940,729,941,473,942,943,425,809,944,945,946,639, 948,569,877,950,951,953,954,603,955,956,957,958,864,960,745,961,833,962,699,541,963,521,965,959,966, 870,738,967,969,707,429,971,972,973,975,970,977,979,968,980,981,439,984,985,915,987,988,990,991,992, 994,996,820,993,930,653,935,918,998,1000,452,1001,457,761,1002,462,1004,867,1006,1007,1008,1009,692,1010,1012, 989,1013,600,853,586,777,675,689,858,565,1016,908,1018,912,730,488,1021,1023,1025,626,531,1026,871,734,510, 825,847,516,1020,512,904,1029,525,1030,638,1024,519,1033,737,665,551,623,1035,534,1036,976,1037,1038,1039,933, 1041,1043,1044,1046,1047,1048,1049,1050,1052,1054,1055,1057,983,1059,1060,1061,1063,1064,557,1065,1066,1067,923,1069,740, 724,1072,1073,1005,702,682,1075,1076,800,1017,1077,1078,855,1079,1080,1082,1070,598,1083,1084,949,947,964,834,1087, 1085,1088,1022,634,1089,897,884,851,1090,668,1092,931,1094,1003,1096,779,1093,1098,1100,1014,677,1071,1102,1062,1031, 1104,1105,1106,1107,1109,1110,672,978,1113,1114,1116,1103,1118,860,997,1121,1122,1123,1124,1125,1095,1126,1128,1129,1068, 705,1130,710,1131,1133,1120,721,1134,752,1028,1027,952,1135,1136,1138,1139,783,1108,1032,890,1140,1086,1099,887,1142, 1143,789,1144,1145,791,1056,1147,1148,1150,1151,1146,1152,823,795,1011,1153,1015,1154,1112,1074,798,995,920,1156,924, 895,1034,974,1157,1158,1160,1137,1161,1162,1097,874,1164,1141,1163,1165,1127,1058,1166,982,1167,1132,894,1169,1119,1170, 1053,1159,899,900,999,1155,1081,1115,1149,1045,1117,1168,1172,1111,1173,1171,1174,1019,1042,986,1175,1176,1040,1051,1101, 1091] >; print "Group G is S4(7) < Sym(1176)";