/* www-ATLAS of Group Representations. S4(7) represented as permutations on 1225 points. */ G:=PermutationGroup<1225|\[ 1,2,3,4,6,5,8,7,10,9,13,14,11,12,18,20,17,15,24,16,27,22,30,19,33, 26,21,36,37,23,40,42,25,45,47,28,29,50,51,31,54,32,43,58,34,61,35,64,66,38, 39,70,72,41,75,76,78,44,81,60,46,83,63,48,65,49,88,68,91,52,71,53,96,98,55, 56,101,57,104,80,59,107,62,110,112,114,115,67,118,120,69,122,124,94,95,73,127,74,130,100, 77,134,136,79,139,141,82,143,145,84,148,85,151,86,87,155,157,89,160,90,121,92,162,93,165, 166,97,169,170,99,173,175,133,102,179,103,137,182,105,185,106,188,108,191,109,193,147,111,195,150, 113,152,199,154,116,203,117,206,207,119,210,123,213,214,125,126,218,220,128,129,223,172,131,227,132, 176,192,229,135,232,234,138,194,184,140,238,187,142,241,242,144,177,146,183,149,248,250,252,153,254, 256,202,156,259,260,158,159,264,209,161,267,269,163,164,215,216,217,167,276,168,279,222,171,283,285, 287,174,290,178,293,295,180,298,181,301,302,303,186,255,307,189,190,311,312,314,316,318,196,320,197, 323,198,326,200,239,201,329,331,204,205,335,337,339,208,342,266,211,344,212,346,348,343,351,274,354, 219,357,278,221,280,360,362,224,365,225,286,226,369,371,228,374,345,230,377,231,379,381,233,384,372, 235,236,237,389,305,391,240,308,394,395,243,244,399,245,402,246,405,247,408,249,409,410,251,413,415, 253,418,420,257,414,258,332,425,427,261,430,262,433,263,436,438,265,272,268,292,270,347,271,444,446, 273,448,449,275,452,454,277,457,459,281,382,282,363,463,284,466,468,469,288,370,289,300,473,291,476, 478,294,481,296,483,297,361,485,299,488,489,491,493,304,496,306,498,499,309,310,503,505,507,313,400, 401,315,511,404,317,514,423,319,321,322,411,518,324,330,325,521,523,327,526,328,527,529,407,531,333, 426,334,535,537,336,539,432,338,542,435,340,437,341,546,547,460,465,549,349,461,350,553,352,353,555, 556,355,559,356,562,564,358,567,359,441,445,506,364,504,442,366,510,367,368,577,579,581,373,582,584, 375,586,376,589,591,378,594,380,484,383,598,600,385,386,604,387,497,388,502,609,390,492,392,393,615, 533,494,396,464,397,462,398,622,624,467,403,627,629,406,632,634,636,412,639,641,416,644,417,645,647, 419,421,650,422,652,424,655,501,534,428,656,429,538,431,658,660,434,663,665,666,439,440,548,443,671, 673,619,447,571,450,451,676,678,453,681,682,455,685,456,565,687,458,688,690,692,554,572,694,695,597, 697,470,698,471,701,472,474,705,475,706,477,709,710,479,713,480,716,717,482,720,722,575,486,724,487, 727,729,731,490,734,735,607,737,495,740,742,744,746,748,500,751,651,753,552,756,757,508,623,509,761, 626,512,765,513,739,768,515,771,516,773,517,775,776,519,779,520,782,784,522,524,646,525,648,649,528, 617,530,791,793,532,536,657,540,798,541,801,764,543,664,544,545,805,668,670,669,550,809,551,674,675, 557,677,558,814,680,560,561,819,684,563,822,566,568,825,569,827,570,829,573,574,804,576,578,834,760, 580,835,837,704,583,585,842,843,587,588,847,849,590,714,851,592,593,718,856,595,721,596,860,599,725, 726,601,728,602,865,603,868,870,605,606,874,608,738,630,610,741,611,879,612,882,613,884,614,749,887, 616,890,618,891,755,620,621,889,841,700,625,762,763,662,628,900,901,631,904,770,633,875,635,908,637, 638,777,778,640,913,914,642,915,643,785,786,892,788,789,790,653,922,654,924,852,926,797,659,799,800, 661,823,930,696,667,933,935,937,672,940,811,812,942,679,944,946,948,950,683,952,953,686,802,858,689, 958,691,828,693,947,963,895,965,699,702,969,703,971,934,973,759,707,708,844,976,979,711,981,712,959, 715,795,918,916,867,719,862,824,859,723,861,857,896,992,730,993,855,732,972,733,995,997,998,736,772, 1000,877,1002,743,1005,1006,745,1008,747,905,1010,750,888,758,752,754,787,893,1015,832,863,1016,1017,1019,766, 767,987,957,769,885,912,907,774,1013,1028,1030,906,780,781,783,854,994,853,1036,1038,1020,792,1034,794,1042, 796,1043,928,1045,803,961,1047,806,839,807,936,808,938,939,810,956,813,943,815,945,816,830,817,1057,818, 1050,820,821,954,955,941,903,826,850,1058,931,1066,831,1069,833,1011,1071,968,836,1073,838,869,840,1029,1079, 845,1082,1084,846,1087,848,982,1089,1091,1093,1095,902,1096,1097,1098,1044,864,866,917,871,1101,872,873,1104,876, 1088,878,1092,1004,880,881,1007,883,1037,886,966,1113,909,1049,894,897,898,1022,899,921,1107,1018,1023,1024,1121, 1033,1123,910,974,911,1031,1032,1026,923,1128,919,1009,920,1078,1132,1133,925,927,991,929,1046,932,1065,1014,951, 1081,1140,1142,1054,1055,1056,949,960,1143,1060,1137,1141,1063,1146,1048,962,1147,1070,964,1068,967,1072,970,1149,1151, 1076,1136,1039,975,1152,1051,977,1083,978,1085,1155,980,1001,983,1090,984,1003,985,1094,986,988,989,990,1099,1100, 996,1164,1165,999,1105,1169,1021,1117,1109,1172,1174,1119,1012,1114,1176,1178,1108,1160,1112,1120,1025,1180,1027,1158,1182, 1183,1184,1035,1161,1187,1188,1040,1041,1134,1189,1077,1061,1138,1190,1052,1062,1053,1059,1166,1194,1064,1067,1196,1074,1198, 1075,1080,1153,1199,1086,1156,1157,1124,1200,1118,1129,1173,1163,1102,1103,1144,1197,1168,1106,1170,1171,1110,1162,1111,1175, 1115,1177,1116,1179,1122,1205,1125,1126,1127,1185,1186,1130,1131,1135,1139,1191,1192,1213,1145,1215,1148,1167,1150,1154,1159, 1209,1202,1203,1204,1181,1214,1220,1208,1201,1210,1211,1212,1193,1206,1195,1221,1217,1218,1222,1207,1216,1219,1223,1224,1225] ,\[ 2,3,4,5,1,7,9,6,11,12,8,15,16,17,19,21,22,23,25,26,28,29,31,32,10, 34,35,37,38,39,41,43,44,46,48,49,13,14,52,53,55,56,57,59,60,62,63,65,67,68, 69,71,73,74,18,77,79,80,45,33,82,20,84,85,86,87,89,90,92,93,94,95,97,88,99, 100,102,103,24,105,106,108,109,111,113,27,116,117,119,91,121,123,125,30,70,126,128,129,131,132, 133,135,137,138,140,142,120,144,146,147,149,150,152,153,154,156,158,159,36,161,50,81,163,164,72, 167,168,40,171,172,174,176,177,178,42,180,181,183,184,186,187,189,190,192,76,110,83,194,47,196, 197,198,200,201,202,204,205,54,208,209,211,212,51,215,216,217,219,195,221,222,224,225,226,175,75, 145,228,230,231,233,235,236,139,104,237,58,239,240,122,243,244,61,245,246,247,249,251,64,253,255, 238,257,258,66,261,262,263,265,266,160,268,270,271,210,272,273,274,275,277,278,280,281,282,284,286, 288,289,291,292,294,296,297,299,300,78,264,304,305,306,308,309,310,241,313,315,317,319,220,321,322, 324,325,327,328,256,114,330,332,333,334,336,338,340,341,343,214,213,107,345,347,349,350,352,353,355, 356,96,269,358,359,361,363,364,98,366,367,368,370,372,373,101,375,376,378,199,380,382,383,385,386, 387,388,193,390,115,392,260,393,143,396,397,398,400,401,403,404,406,407,127,374,112,411,412,414,416, 417,419,421,185,422,423,424,426,428,429,431,432,434,435,437,439,440,118,441,248,357,442,443,445,124, 447,449,450,451,453,455,456,458,360,169,460,461,462,464,465,467,130,470,471,472,433,314,474,475,477, 479,480,134,482,381,179,484,486,487,136,490,492,494,495,329,497,141,500,501,502,504,506,508,509,510, 227,488,303,512,513,148,335,515,491,516,517,519,520,151,496,522,524,525,295,481,528,155,530,532,533, 427,534,536,538,529,157,540,541,466,365,543,544,545,182,454,548,162,550,551,267,552,554,553,165,166, 557,558,560,561,563,565,566,568,569,170,570,571,351,572,573,206,574,575,576,578,580,173,542,583,585, 311,587,588,590,592,593,595,596,597,285,599,601,602,603,605,606,493,607,608,610,611,612,613,614,188, 616,617,618,555,619,620,621,623,625,191,626,628,630,631,633,635,637,638,640,642,643,523,252,646,648, 649,371,651,377,653,654,203,457,259,644,307,498,318,657,659,661,662,664,207,667,668,669,670,283,672, 674,448,675,556,242,463,677,679,680,218,683,684,636,686,647,645,615,689,691,693,223,549,339,485,696, 579,567,699,700,702,703,704,688,469,707,708,229,711,712,714,715,430,718,719,721,723,232,705,725,726, 728,730,732,733,234,736,301,738,739,741,743,745,747,749,750,697,752,754,755,476,665,758,759,760,762, 763,764,766,731,767,769,770,720,772,774,276,250,777,778,780,781,783,785,786,425,694,346,787,788,789, 254,790,792,794,795,796,701,797,799,800,527,546,687,802,803,804,806,473,807,737,808,810,666,811,446, 682,812,813,815,816,817,818,342,820,821,823,824,290,279,826,828,594,830,326,831,757,832,833,287,584, 658,836,838,839,840,841,320,844,845,846,848,850,773,293,852,853,854,855,857,858,859,771,861,862,298, 863,660,864,837,866,867,869,871,872,873,875,344,302,634,876,877,878,880,881,883,507,885,886,641,888, 889,843,756,892,893,894,895,655,312,896,489,897,898,581,899,316,902,903,652,905,906,907,904,822,909, 847,910,911,912,323,499,632,916,917,918,919,920,805,921,514,629,331,923,798,925,900,539,927,337,924, 928,929,746,931,932,934,936,938,939,348,941,354,943,673,945,947,949,951,505,734,954,410,955,956,957, 959,960,961,962,362,964,394,966,967,968,369,970,627,972,974,975,976,395,977,978,887,980,982,983,884, 984,985,986,987,420,988,989,408,379,990,935,624,991,384,879,402,994,926,761,856,996,562,901,999,409, 1001,389,1003,1004,415,681,1007,391,1009,537,1011,882,577,1008,1012,1013,1014,819,860,468,724,399,1018,1020,1021, 1022,405,695,1023,1024,1025,609,1026,1027,1029,1031,748,1032,1033,958,413,1034,1035,1037,418,1039,1005,1040,1041,622, 930,531,1044,436,1046,814,526,1038,438,483,1048,1049,1050,1051,908,444,676,1052,1053,452,1054,1055,1056,744,1006, 942,1058,1059,1060,1061,1062,915,1063,1064,1065,459,1067,1068,768,1070,1042,801,716,1072,1074,1075,1076,1077,1078,1080, 1081,1083,1085,1086,1088,775,478,1090,1092,1094,835,971,913,692,753,1099,1100,742,791,965,1102,1103,952,1105,1106, 1107,740,1108,1109,1110,842,710,1111,589,1112,779,1114,1115,503,946,1116,1117,511,998,1118,1119,1120,1091,782,1122, 1096,1124,1125,518,1126,1101,870,1036,1127,521,1129,535,1130,1131,969,727,1134,751,834,1135,1136,940,547,1137,1138, 1139,1141,1015,944,559,829,890,1097,1144,1145,564,663,825,1066,1142,690,948,979,1148,1016,851,793,1132,1150,717, 582,1045,598,1010,1153,950,1147,586,1154,1155,1156,1057,1157,1158,1159,713,1160,1161,591,1162,1047,1019,1163,600,1073, 639,604,1166,1167,1168,1170,1002,993,1171,1173,1043,1175,1079,1087,1177,995,1069,1179,656,735,1178,722,1181,981,953, 1123,1185,1186,1174,1121,650,1151,1095,698,1183,868,1140,671,1189,1191,678,1192,1193,1028,685,1030,1195,1197,1133,729, 992,1188,706,1200,709,963,776,1201,1164,1071,1202,1203,1204,849,1199,1205,1206,1169,874,1207,865,1208,1184,914,1113, 1209,1210,933,765,1211,1146,1000,973,922,784,1093,1176,1212,809,1082,937,827,1180,1214,1216,1084,1017,1217,1152,1218, 1194,1128,1149,1213,1219,1220,1182,1198,1221,891,1215,1165,1222,1089,1143,1190,1223,1196,997,1224,1225,1098,1172,1104,1187] >; print "Group G is S4(7) < Sym(1225)";