/* www-ATLAS of Group Representations. S15 represented as permutations on 1365 points. */ G:=PermutationGroup<1365|\[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50, 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75, 76,77,78,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386, 387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411, 412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436, 437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461, 462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486, 487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511, 512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536, 537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561, 562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586, 587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611, 612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636, 637,638,639,640,641,642,643,644,645,646,647,648,649,650,79,80,81,82,83,84,85,86,87,88,89, 90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114, 115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139, 140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164, 165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189, 190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214, 215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239, 240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264, 265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289, 290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314, 315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339, 340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364, 651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675, 676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700, 701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725, 726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750, 751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775, 776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800, 801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825, 826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850, 851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875, 876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900, 901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925, 926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950, 951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975, 976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000, 1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025, 1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050, 1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075, 1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100, 1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125, 1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150, 1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175, 1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200, 1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225, 1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250, 1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275, 1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300, 1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325, 1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350, 1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365] ,\[ 12,23,33,42,50,57,63,68,72,75,77,78,89,99,108,116,123,129,134,138,141,143,144,154,163, 171,178,184,189,193,196,198,199,208,216,223,229,234,238,241,243,244,252,259,265,270,274,277,279,280, 287,293,298,302,305,307,308,314,319,323,326,328,329,334,338,341,343,344,348,351,353,354,357,359,360, 362,363,364,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,24, 25,26,27,28,29,30,31,32,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,51,52, 53,54,55,56,58,59,60,61,62,64,65,66,67,69,70,71,73,74,76,79,80,81,82,83,84, 85,86,87,88,90,91,92,93,94,95,96,97,98,100,101,102,103,104,105,106,107,109,110,111,112, 113,114,115,117,118,119,120,121,122,124,125,126,127,128,130,131,132,133,135,136,137,139,140,142,145, 146,147,148,149,150,151,152,153,155,156,157,158,159,160,161,162,164,165,166,167,168,169,170,172,173, 174,175,176,177,179,180,181,182,183,185,186,187,188,190,191,192,194,195,197,200,201,202,203,204,205, 206,207,209,210,211,212,213,214,215,217,218,219,220,221,222,224,225,226,227,228,230,231,232,233,235, 236,237,239,240,242,245,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,263,264,266,267, 268,269,271,272,273,275,276,278,281,282,283,284,285,286,288,289,290,291,292,294,295,296,297,299,300, 301,303,304,306,309,310,311,312,313,315,316,317,318,320,321,322,324,325,327,330,331,332,333,335,336, 337,339,340,342,345,346,347,349,350,352,355,356,358,361,375,385,394,402,409,415,420,424,427,429,430, 440,449,457,464,470,475,479,482,484,485,494,502,509,515,520,524,527,529,530,538,545,551,556,560,563, 565,566,573,579,584,588,591,593,594,600,605,609,612,614,615,620,624,627,629,630,634,637,639,640,643, 645,646,648,649,650,660,669,677,684,690,695,699,702,704,705,714,722,729,735,740,744,747,749,750,758, 765,771,776,780,783,785,786,793,799,804,808,811,813,814,820,825,829,832,834,835,840,844,847,849,850, 854,857,859,860,863,865,866,868,869,870,879,887,894,900,905,909,912,914,915,923,930,936,941,945,948, 950,951,958,964,969,973,976,978,979,985,990,994,997,999,1000,1005,1009,1012,1014,1015,1019,1022,1024,1025,1028, 1030,1031,1033,1034,1035,1043,1050,1056,1061,1065,1068,1070,1071,1078,1084,1089,1093,1096,1098,1099,1105,1110,1114,1117,1119, 1120,1125,1129,1132,1134,1135,1139,1142,1144,1145,1148,1150,1151,1153,1154,1155,1162,1168,1173,1177,1180,1182,1183,1189,1194, 1198,1201,1203,1204,1209,1213,1216,1218,1219,1223,1226,1228,1229,1232,1234,1235,1237,1238,1239,1245,1250,1254,1257,1259,1260, 1265,1269,1272,1274,1275,1279,1282,1284,1285,1288,1290,1291,1293,1294,1295,1300,1304,1307,1309,1310,1314,1317,1319,1320,1323, 1325,1326,1328,1329,1330,1334,1337,1339,1340,1343,1345,1346,1348,1349,1350,1353,1355,1356,1358,1359,1360,1362,1363,1364,1365, 365,366,367,368,369,370,371,372,373,374,376,377,378,379,380,381,382,383,384,386,387,388,389,390,391, 392,393,395,396,397,398,399,400,401,403,404,405,406,407,408,410,411,412,413,414,416,417,418,419,421, 422,423,425,426,428,431,432,433,434,435,436,437,438,439,441,442,443,444,445,446,447,448,450,451,452, 453,454,455,456,458,459,460,461,462,463,465,466,467,468,469,471,472,473,474,476,477,478,480,481,483, 486,487,488,489,490,491,492,493,495,496,497,498,499,500,501,503,504,505,506,507,508,510,511,512,513, 514,516,517,518,519,521,522,523,525,526,528,531,532,533,534,535,536,537,539,540,541,542,543,544,546, 547,548,549,550,552,553,554,555,557,558,559,561,562,564,567,568,569,570,571,572,574,575,576,577,578, 580,581,582,583,585,586,587,589,590,592,595,596,597,598,599,601,602,603,604,606,607,608,610,611,613, 616,617,618,619,621,622,623,625,626,628,631,632,633,635,636,638,641,642,644,647,651,652,653,654,655, 656,657,658,659,661,662,663,664,665,666,667,668,670,671,672,673,674,675,676,678,679,680,681,682,683, 685,686,687,688,689,691,692,693,694,696,697,698,700,701,703,706,707,708,709,710,711,712,713,715,716, 717,718,719,720,721,723,724,725,726,727,728,730,731,732,733,734,736,737,738,739,741,742,743,745,746, 748,751,752,753,754,755,756,757,759,760,761,762,763,764,766,767,768,769,770,772,773,774,775,777,778, 779,781,782,784,787,788,789,790,791,792,794,795,796,797,798,800,801,802,803,805,806,807,809,810,812, 815,816,817,818,819,821,822,823,824,826,827,828,830,831,833,836,837,838,839,841,842,843,845,846,848, 851,852,853,855,856,858,861,862,864,867,871,872,873,874,875,876,877,878,880,881,882,883,884,885,886, 888,889,890,891,892,893,895,896,897,898,899,901,902,903,904,906,907,908,910,911,913,916,917,918,919, 920,921,922,924,925,926,927,928,929,931,932,933,934,935,937,938,939,940,942,943,944,946,947,949,952, 953,954,955,956,957,959,960,961,962,963,965,966,967,968,970,971,972,974,975,977,980,981,982,983,984, 986,987,988,989,991,992,993,995,996,998,1001,1002,1003,1004,1006,1007,1008,1010,1011,1013,1016,1017,1018,1020,1021, 1023,1026,1027,1029,1032,1036,1037,1038,1039,1040,1041,1042,1044,1045,1046,1047,1048,1049,1051,1052,1053,1054,1055,1057,1058, 1059,1060,1062,1063,1064,1066,1067,1069,1072,1073,1074,1075,1076,1077,1079,1080,1081,1082,1083,1085,1086,1087,1088,1090,1091, 1092,1094,1095,1097,1100,1101,1102,1103,1104,1106,1107,1108,1109,1111,1112,1113,1115,1116,1118,1121,1122,1123,1124,1126,1127, 1128,1130,1131,1133,1136,1137,1138,1140,1141,1143,1146,1147,1149,1152,1156,1157,1158,1159,1160,1161,1163,1164,1165,1166,1167, 1169,1170,1171,1172,1174,1175,1176,1178,1179,1181,1184,1185,1186,1187,1188,1190,1191,1192,1193,1195,1196,1197,1199,1200,1202, 1205,1206,1207,1208,1210,1211,1212,1214,1215,1217,1220,1221,1222,1224,1225,1227,1230,1231,1233,1236,1240,1241,1242,1243,1244, 1246,1247,1248,1249,1251,1252,1253,1255,1256,1258,1261,1262,1263,1264,1266,1267,1268,1270,1271,1273,1276,1277,1278,1280,1281, 1283,1286,1287,1289,1292,1296,1297,1298,1299,1301,1302,1303,1305,1306,1308,1311,1312,1313,1315,1316,1318,1321,1322,1324,1327, 1331,1332,1333,1335,1336,1338,1341,1342,1344,1347,1351,1352,1354,1357,1361] >; print "Group G is S15 < Sym(1365)";