/* www-ATLAS of Group Representations. 12a.L3(4) represented as permutations on 1440 points. */ G:=PermutationGroup<1440|\[ 1,8,3,4,20,6,7,2,30,25,26,28,29,14,15,44,17,46,19,5,50,51,23,53,10, 11,48,12,13,9,69,70,72,73,59,60,62,64,67,40,82,42,84,16,87,18,90,27,94,21, 22,97,24,104,99,100,102,103,35,36,85,37,88,38,92,93,39,121,31,32,133,33,34,127,128, 130,132,136,114,116,139,41,142,43,61,147,45,63,151,47,153,65,66,49,159,160,52,162,55,56, 174,57,58,54,179,180,182,183,168,169,171,173,177,79,140,80,143,146,150,156,68,199,194,195,197, 198,74,75,213,76,215,77,71,218,193,78,209,211,81,115,224,83,117,227,228,118,86,232,233,119, 89,237,91,240,241,120,243,247,95,96,250,98,257,252,253,255,256,109,110,271,111,273,112,101,277, 278,113,280,105,106,292,107,108,286,287,289,291,295,267,269,220,223,135,123,124,307,125,126,122,312, 313,314,315,301,302,304,306,310,137,324,138,326,129,299,131,329,330,134,300,191,333,334,192,141,338, 339,144,145,344,345,348,148,149,352,353,356,152,358,362,154,155,365,157,370,368,369,158,375,251,161, 249,164,165,386,166,167,163,391,392,394,395,380,381,383,385,389,189,404,190,406,170,409,172,412,413, 417,175,176,420,178,359,422,423,425,426,184,185,440,186,442,187,181,446,447,188,436,438,449,214,219, 204,205,457,206,459,207,196,463,464,208,466,200,201,202,203,471,472,473,474,475,453,455,478,210,452, 212,481,482,216,217,486,487,221,222,492,493,496,225,226,500,502,503,506,229,230,511,510,231,378,514, 517,234,235,522,521,236,525,238,281,528,529,239,535,536,242,538,542,245,246,244,546,547,545,549,248, 379,551,349,376,262,263,559,264,561,265,254,565,566,266,568,258,259,467,260,261,573,574,576,578,580, 555,557,583,268,585,270,588,418,272,592,595,274,275,601,599,600,276,408,606,279,608,282,283,424,284, 285,504,515,530,531,614,615,617,619,622,296,631,297,633,288,636,290,639,640,558,293,294,563,298,645, 647,325,321,650,322,652,303,597,305,656,657,594,308,309,662,311,393,663,664,665,316,317,318,319,320, 671,672,323,674,675,327,328,680,681,684,331,332,688,690,691,694,335,336,698,697,337,554,701,703,340, 706,341,342,427,710,343,714,540,717,347,346,719,720,350,428,722,351,726,727,730,355,354,732,733,357, 552,737,360,361,429,430,740,533,745,363,364,748,366,751,508,750,367,678,676,373,371,372,756,374,758, 377,526,760,497,401,763,402,445,382,638,384,767,448,770,387,388,773,390,775,776,778,779,396,397,666, 398,667,399,668,400,785,786,403,790,405,792,596,407,797,796,607,410,800,462,411,587,458,804,415,416, 414,809,810,655,812,419,591,421,820,815,816,818,819,431,432,616,433,618,434,620,621,435,692,702,711, 723,741,830,832,839,437,769,439,843,762,441,846,560,443,444,853,851,852,731,450,858,451,856,860,454, 794,456,863,864,604,460,461,870,868,869,789,465,468,469,470,575,577,579,873,874,476,477,877,479,480, 544,881,543,883,483,484,805,886,485,888,889,891,488,893,489,490,623,896,491,900,882,495,494,901,902, 498,624,499,729,907,501,736,761,910,505,625,712,914,507,916,754,509,878,512,513,920,516,626,724,924, 518,519,927,704,520,644,523,524,931,932,707,527,936,937,532,627,939,743,744,534,945,946,537,948,541, 539,952,953,716,799,548,954,550,956,553,708,635,556,842,959,960,562,962,632,564,966,967,567,969,569, 570,981,571,572,975,976,978,980,984,581,582,875,876,661,584,867,586,989,651,991,590,589,993,755,593, 996,997,998,598,682,929,999,1002,602,603,1005,605,814,813,610,611,911,612,613,609,1013,1014,1016,1017,1004, 1003,1009,934,1011,628,831,629,833,834,835,836,890,897,630,1027,943,764,634,1031,1030,637,1034,1033,1035,947, 642,643,641,865,892,648,1042,646,1043,649,1045,1046,653,654,854,1047,791,659,660,658,1050,1049,669,670,787, 788,673,718,1052,1053,677,696,679,1054,1055,683,987,685,686,837,687,855,689,909,1059,693,838,898,1063,695, 699,700,1010,904,1067,1068,705,1070,894,709,817,1072,913,713,1076,715,1077,988,1078,721,1080,1015,923,725,1037, 944,728,1075,806,1084,734,735,1088,828,1089,738,739,1091,742,1093,1094,942,841,926,746,747,850,749,1082,1064, 1098,752,753,757,1103,759,1106,1107,765,766,1112,768,1113,1114,1118,771,772,1121,774,970,1123,1124,1126,1127,780, 781,1141,782,1143,783,777,1147,1148,784,1137,1139,887,918,793,1150,795,1069,798,1151,1023,801,802,803,807,1155, 1156,808,826,825,811,1159,1160,1060,827,903,829,1162,821,822,922,823,824,1168,1169,1171,1172,1174,995,1024,1025, 1074,840,1176,1177,845,844,1181,848,847,849,1185,925,1186,1188,1048,1189,857,859,1190,861,862,866,1040,872,871, 1191,879,880,884,885,1161,1057,1097,895,1008,1194,1062,899,950,1196,1170,905,906,992,908,1199,912,1201,1026,928, 915,917,919,1205,921,1173,949,1154,930,1208,1209,1212,933,935,1184,938,1214,940,941,1217,1218,1058,951,1219,1220, 1221,1224,955,1226,1229,957,958,1233,1234,1235,1238,961,963,964,1215,1240,1241,965,1246,1122,968,1120,971,972,1257, 973,974,1128,1129,1130,1131,1251,1252,1254,1256,1260,985,1269,986,1271,977,1274,979,1276,1277,1206,982,983,1282,990, 994,1283,1284,1083,1000,1001,1286,1287,1006,1007,1056,1012,1187,1288,1289,1222,1210,1018,1019,1066,1020,1021,1081,1022,1298, 1028,1029,1301,1302,1304,1032,1305,1249,1090,1036,1038,1163,1039,1041,1044,1051,1308,1297,1061,1310,1065,1313,1316,1071,1318, 1073,1285,1320,1321,1079,1146,1324,1085,1086,1167,1273,1087,1327,1092,1115,1306,1095,1096,1099,1100,1101,1166,1330,1102,1332, 1104,1296,1334,1105,1336,1337,1338,1108,1109,1110,1291,1340,1111,1343,1116,1117,1309,1328,1344,1346,1119,1250,1348,1183,1247, 1132,1133,1258,1134,1356,1135,1125,1253,1359,1136,1261,1262,1263,1264,1265,1352,1353,1363,1138,1365,1140,1279,1211,1142,1369, 1144,1145,1373,1272,1372,1323,1149,1152,1153,1202,1157,1158,1164,1165,1303,1236,1331,1377,1314,1322,1227,1193,1175,1380,1351, 1178,1179,1290,1180,1182,1216,1383,1192,1242,1195,1385,1386,1197,1294,1364,1198,1388,1200,1381,1203,1204,1295,1281,1207,1391, 1392,1213,1243,1393,1223,1292,1225,1395,1228,1379,1230,1231,1232,1398,1237,1378,1399,1239,1244,1384,1245,1402,1248,1404,1405, 1300,1266,1267,1357,1360,1255,1354,1406,1259,1355,1361,1362,1268,1315,1270,1370,1407,1375,1275,1366,1408,1280,1278,1411,1368, 1390,1293,1341,1335,1299,1319,1412,1307,1345,1311,1312,1414,1317,1415,1376,1325,1326,1329,1418,1333,1420,1421,1339,1342,1424, 1410,1347,1417,1349,1350,1358,1367,1371,1431,1401,1374,1382,1416,1387,1389,1413,1403,1394,1423,1396,1397,1429,1419,1400,1432, 1435,1436,1440,1422,1438,1409,1425,1434,1433,1426,1427,1439,1430,1437,1428] ,\[ 2,9,10,11,1,12,13,24,5,31,32,33,34,35,36,3,37,4,38,48,6,7,39,54,55, 56,8,57,58,68,16,18,21,22,74,75,76,77,78,79,14,80,15,85,17,88,19,91,20,92, 93,23,98,27,105,106,107,108,109,110,25,111,26,112,28,29,113,122,123,124,30,125,126,41,43, 45,47,52,137,138,40,140,42,143,145,44,146,149,46,150,49,154,155,157,50,51,156,163,164,165, 53,166,167,178,61,63,65,66,184,185,186,187,188,189,59,190,60,62,64,67,193,71,200,201,202, 203,204,205,69,206,70,207,217,72,73,208,81,83,220,222,82,223,226,84,86,229,230,87,89,234, 235,90,238,95,96,242,244,94,245,246,97,251,101,258,259,260,261,262,263,99,264,100,265,275,102, 103,266,281,282,283,104,284,285,115,117,118,119,120,296,297,114,116,298,299,133,121,300,215,311,129, 131,134,135,316,317,318,319,320,321,127,322,128,327,130,328,132,305,331,136,332,139,141,335,336,142, 144,340,342,148,346,147,347,350,152,354,151,355,359,153,360,361,161,366,158,371,372,374,159,160,373, 377,378,247,162,379,356,390,170,172,175,176,396,397,398,399,400,401,168,402,169,407,171,410,173,414, 174,415,416,177,421,181,427,428,429,430,431,432,179,433,180,434,444,182,183,435,191,192,196,450,451, 452,213,194,326,195,218,461,197,198,329,199,467,468,469,470,210,212,214,216,219,476,477,209,479,211, 480,456,309,483,484,460,221,488,490,225,494,224,495,498,501,227,504,228,505,508,231,512,513,232,515, 233,516,519,236,523,524,237,526,239,530,531,533,240,241,532,539,243,540,541,393,248,249,548,384,550, 250,254,552,553,554,348,252,502,253,375,563,255,256,525,370,569,570,257,571,572,268,270,272,274,279, 581,582,267,584,269,586,589,271,590,593,273,594,597,276,602,603,404,277,278,604,609,610,611,280,612, 613,288,290,293,294,623,624,625,626,627,628,286,629,287,634,289,637,291,641,292,642,643,295,644,303, 308,648,324,301,478,302,653,304,654,306,658,307,659,660,310,394,312,313,314,315,666,667,668,669,670, 323,325,673,649,458,676,678,465,682,330,683,686,689,333,692,334,693,538,337,699,700,338,702,339,704, 341,707,708,343,711,712,344,715,345,716,575,349,558,720,351,723,724,352,728,353,729,577,357,388,734, 735,358,551,736,363,364,741,742,362,743,744,365,749,367,752,753,755,368,369,754,466,579,376,757,562, 759,382,387,761,496,380,690,381,447,383,446,385,768,386,769,639,389,774,511,522,546,547,780,781,391, 782,392,783,395,784,403,405,789,605,791,793,406,794,408,798,409,457,411,801,583,412,803,413,464,652, 807,418,419,811,417,585,420,814,424,821,822,823,824,825,826,422,827,423,828,425,426,829,437,439,441, 443,448,837,838,436,840,438,841,844,440,845,847,442,848,849,445,766,765,854,730,449,855,454,453,861, 455,862,799,865,459,866,868,462,871,805,463,872,578,573,580,471,472,473,474,475,875,876,651,878,542, 804,481,870,482,882,545,485,887,881,486,890,487,727,489,894,760,491,897,898,492,493,750,664,497,762, 902,499,904,906,500,787,560,908,503,909,507,912,506,913,509,917,918,510,788,919,514,549,518,922,517, 923,926,520,928,929,521,663,930,567,527,933,934,528,529,733,537,534,940,941,943,535,536,942,696,949, 950,543,544,885,880,665,921,955,738,957,556,555,636,557,559,561,631,564,963,964,565,566,839,970,971, 972,568,973,974,698,706,719,732,756,985,986,574,576,802,662,813,650,587,990,588,860,935,591,592,994, 596,595,598,677,599,600,936,601,1000,1001,607,1006,606,1007,1005,812,608,993,997,1012,616,618,620,621,1018, 1019,1020,1021,1022,1002,614,1023,615,617,619,622,630,632,1026,961,1028,633,1029,635,958,1032,638,772,916,640, 951,1036,1038,646,1040,907,645,1042,647,1044,988,806,657,1047,655,1048,656,1045,1049,679,661,987,785,786,671, 672,717,991,674,675,1052,1050,1053,680,681,697,685,684,758,687,1057,688,873,764,691,931,695,1061,694,1062, 874,1065,701,1066,703,705,1069,709,1071,816,710,713,1073,1074,714,850,718,1051,721,1011,722,725,1081,1030,726, 892,1063,731,857,938,1085,1086,739,797,737,808,818,740,1017,746,747,1095,1096,745,846,843,748,946,886,851, 751,1076,1097,1101,1056,1104,895,763,1108,1110,767,1100,771,1115,770,1116,1117,773,1122,777,1128,1129,1130,1131,1132, 1133,775,1134,776,1135,1145,778,779,1136,893,901,790,792,1079,795,879,796,1090,1080,800,1152,1153,869,1154,1059, 1091,1158,809,810,1157,910,817,815,996,819,989,1163,1164,1165,820,1166,1167,831,833,834,835,836,1175,830,832, 968,1099,842,948,1178,1179,1068,1083,1182,1184,1077,852,1187,853,859,856,1189,858,992,863,864,1190,867,1150,884, 877,888,1191,883,1067,889,1193,891,1003,896,899,1195,1033,900,903,905,1113,945,1041,1197,911,1171,915,1202,914, 1027,1037,1203,920,995,925,924,927,1206,1060,1210,932,1211,1181,937,1004,939,1174,1014,947,944,962,1156,952,953, 1222,954,1223,1227,956,1228,1231,1214,959,1236,960,1237,1192,1240,965,1242,1243,1245,966,967,1244,1248,1249,1118,969, 1250,1238,977,979,982,983,1261,1262,1263,1264,1265,1266,975,1267,976,1272,978,1275,980,1278,981,1279,1280,984,998, 1220,1161,1010,999,1285,1098,1008,1024,1218,1177,1009,1204,1015,1290,1216,1291,1092,1292,1293,1013,1294,1295,1016,1296,1025, 1299,1160,1082,1303,1031,1089,1306,1034,1035,1205,1235,1039,1307,1043,1046,1054,1055,1058,1298,1064,1311,1314,1070,1315,1072, 1169,1075,1162,1078,1185,1322,1084,1323,1271,1087,1289,1316,1088,1109,1093,1094,1172,1159,1286,1151,1148,1102,1331,1321,1103, 1143,1105,1335,1212,1106,1318,1107,1114,1339,1340,1111,1341,1342,1112,1337,1344,1119,1120,1345,1255,1347,1121,1125,1349,1350, 1351,1234,1123,1188,1124,1246,1251,1126,1127,1343,1138,1140,1142,1144,1149,1361,1362,1137,1277,1139,1366,1367,1141,1368,1333, 1370,1371,1146,1374,1329,1147,1375,1308,1301,1155,1219,1376,1312,1213,1170,1173,1378,1319,1200,1328,1215,1168,1379,1381,1176, 1284,1186,1180,1382,1241,1183,1355,1283,1194,1287,1288,1196,1363,1198,1377,1336,1199,1232,1201,1274,1386,1207,1390,1327,1208, 1209,1388,1217,1221,1282,1225,1224,1226,1276,1230,1229,1233,1397,1354,1302,1239,1259,1400,1380,1247,1401,1357,1403,1253,1258, 1358,1338,1304,1252,1254,1352,1256,1257,1353,1260,1268,1270,1369,1269,1372,1326,1273,1389,1387,1396,1364,1409,1399,1281,1394, 1384,1317,1297,1309,1305,1300,1359,1413,1310,1365,1332,1313,1391,1320,1325,1324,1404,1346,1330,1348,1334,1356,1422,1423,1360, 1417,1425,1419,1426,1427,1428,1383,1412,1385,1373,1424,1433,1429,1406,1398,1392,1393,1402,1395,1405,1438,1435,1410,1439,1436, 1416,1437,1434,1407,1408,1421,1411,1430,1414,1415,1418,1420,1440,1432,1431] >; print "Group G is 12a.L3(4) < Sym(1440)";