/* www-ATLAS of Group Representations. U3(4) represented as permutations on 1600 points. */ G:=PermutationGroup<1600|\[ 2,1,5,6,3,4,11,12,13,14,7,8,9,10,23,24,25,26,27,28,29,30,15,16,17, 18,19,20,21,22,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,31,32,33,34, 35,36,37,38,39,40,41,42,43,44,45,46,90,91,92,93,94,95,96,97,98,99,100,101,102, 103,104,105,106,107,108,109,110,111,112,113,114,115,116,63,64,65,66,67,68,69,70,71,72,73, 74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,158,159,160,161,162,163,164,165,166, 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, 192,193,194,195,196,197,198,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134, 135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,276,277, 278,279,280,281,282,237,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301, 302,303,304,305,306,307,308,309,310,311,312,206,313,314,315,316,317,318,319,320,321,322,323,324,325, 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, 199,200,201,202,203,204,205,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224, 225,226,227,228,229,230,231,232,233,234,235,236,238,239,240,241,242,243,244,245,246,247,248,249,250, 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, 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, 496,497,431,498,499,500,501,502,407,503,387,386,404,504,505,470,506,507,508,509,510,511,512,513,514, 515,516,432,388,517,518,384,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536, 537,538,539,540,541,378,403,542,543,544,545,447,546,547,441,440,548,549,550,551,552,437,553,554,555, 556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,391,351,352,353,354,355, 356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,379,380,381, 382,383,385,389,390,392,393,394,395,396,397,398,399,400,401,402,405,406,408,409,410,411,412,413,414, 415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,433,434,435,436,438,439,442,443,444, 445,446,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,721, 722,723,662,631,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,712,741,742,743, 744,745,650,688,746,747,608,607,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,651,763, 764,765,660,766,767,579,654,768,769,770,771,772,773,678,667,676,774,775,776,777,778,779,780,781,603, 624,782,783,632,784,785,786,787,788,628,789,578,790,791,792,793,640,794,795,796,797,798,799,800,801, 641,802,639,803,804,805,806,807,808,809,810,811,604,812,691,690,813,814,815,816,817,818,819,820,821, 822,823,824,705,704,825,826,827,828,829,830,597,831,832,833,834,835,836,837,838,575,576,577,580,581, 582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,598,599,600,601,602,605,606,609,610,611, 612,613,614,615,616,617,618,619,620,621,622,623,625,626,627,629,630,633,634,635,636,637,638,642,643, 644,645,646,647,648,649,652,653,655,656,657,658,659,661,663,664,665,666,668,669,670,671,672,673,674, 675,677,679,680,681,682,683,684,685,686,687,689,692,693,694,695,696,697,698,699,700,701,702,703,706, 707,708,709,710,711,713,714,715,716,717,718,719,720,1007,1008,855,1009,1010,863,1011,1012,1013,1014,1015,1016, 1017,917,884,1018,841,890,1019,1020,867,1021,1022,1023,844,871,866,865,859,932,1024,1025,864,1026,938,1027,1028, 912,1029,1030,939,1031,1032,1033,1034,853,1035,1036,1037,1038,1039,856,1040,893,892,1041,1042,1043,1044,962,1045,1046, 1047,1048,1049,1050,1051,1052,1053,1003,1054,1055,1056,876,965,1057,1058,1059,852,1060,1061,1062,1063,1064,1065,1066,1067, 1068,990,1069,1070,1071,1072,868,954,1073,1074,1075,1076,873,879,1077,1078,1079,964,1006,1080,1081,1082,1083,1084,1085, 1086,1087,1088,933,1089,1090,1091,993,1092,1093,1094,898,1095,943,913,1096,1097,1098,1099,1100,1101,1102,987,1103,1104, 1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,973,989,988,927,1116,1117,958,1118,1119,1120,1121,1122,1123,1124, 1125,1126,908,1127,1128,944,839,840,842,843,845,846,847,848,849,850,851,854,857,858,860,861,862,869,870, 872,874,875,877,878,880,881,882,883,885,886,887,888,889,891,894,895,896,897,899,900,901,902,903,904, 905,906,907,909,910,911,914,915,916,918,919,920,921,922,923,924,925,926,928,929,930,931,934,935,936, 937,940,941,942,945,946,947,948,949,950,951,952,953,955,956,957,959,960,961,963,966,967,968,969,970, 971,972,974,975,976,977,978,979,980,981,982,983,984,985,986,991,992,994,995,996,997,998,999,1000,1001, 1002,1004,1005,1256,1277,1278,1242,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296, 1297,1227,1230,1298,1184,1202,1299,1166,1300,1177,1301,1302,1235,1303,1213,1158,1304,1305,1306,1307,1308,1309,1310,1311,1312, 1313,1160,1314,1315,1316,1317,1318,1319,1155,1320,1275,1321,1322,1231,1323,1207,1324,1325,1326,1211,1223,1217,1327,1328,1329, 1330,1156,1331,1332,1333,1334,1191,1335,1336,1264,1195,1337,1165,1338,1339,1340,1197,1341,1342,1343,1344,1345,1196,1346,1347, 1348,1152,1349,1239,1153,1189,1350,1351,1352,1163,1353,1354,1355,1229,1356,1357,1132,1358,1260,1359,1360,1361,1362,1363,1364, 1365,1366,1367,1368,1369,1129,1266,1370,1371,1244,1372,1373,1374,1210,1274,1257,1375,1376,1377,1378,1379,1380,1381,1265,1186, 1382,1130,1131,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1154,1157,1159, 1161,1162,1164,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1178,1179,1180,1181,1182,1183,1185,1187,1188,1190,1192,1193, 1194,1198,1199,1200,1201,1203,1204,1205,1206,1208,1209,1212,1214,1215,1216,1218,1219,1220,1221,1222,1224,1225,1226,1228,1232, 1233,1234,1236,1237,1238,1240,1241,1243,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1258,1259,1261,1262,1263,1267, 1268,1269,1270,1271,1272,1273,1276,1491,1431,1492,1493,1494,1495,1461,1448,1496,1497,1498,1499,1432,1402,1500,1464,1501,1502, 1503,1396,1452,1504,1505,1444,1486,1445,1506,1413,1484,1465,1410,1422,1507,1508,1509,1510,1511,1512,1513,1414,1514,1515,1516, 1517,1518,1519,1520,1459,1384,1395,1521,1522,1471,1523,1489,1490,1462,1524,1525,1526,1527,1406,1408,1528,1469,1390,1475,1529, 1480,1403,1530,1472,1466,1481,1483,1531,1430,1532,1389,1439,1533,1398,1412,1455,1487,1534,1447,1535,1435,1454,1474,1473,1449, 1536,1537,1538,1539,1451,1456,1540,1457,1411,1541,1407,1467,1542,1437,1438,1383,1385,1386,1387,1388,1391,1392,1393,1394,1397, 1399,1400,1401,1404,1405,1409,1415,1416,1417,1418,1419,1420,1421,1423,1424,1425,1426,1427,1428,1429,1433,1434,1436,1440,1441, 1442,1443,1446,1450,1453,1458,1460,1463,1468,1470,1476,1477,1478,1479,1482,1485,1488,1569,1573,1556,1574,1572,1575,1557,1570, 1566,1576,1560,1577,1578,1545,1549,1579,1580,1553,1581,1582,1583,1584,1585,1551,1586,1587,1543,1550,1588,1547,1544,1546,1548, 1552,1554,1555,1558,1559,1561,1562,1563,1564,1565,1567,1568,1571,1594,1595,1592,1591,1596,1589,1590,1593,1598,1597,1600,1599] ,\[ 1,3,4,2,7,9,8,5,10,6,15,17,19,21,16,11,18,12,20,13,22,14,31,33,35, 37,39,41,43,45,32,23,34,24,36,25,38,26,40,27,42,28,44,29,46,30,63,65,67,69, 71,57,53,74,76,78,73,80,82,84,86,88,64,47,66,48,68,49,70,50,72,51,52,75,54, 77,55,79,56,81,58,83,59,85,60,87,61,89,62,117,119,121,122,124,111,126,115,129,131,133, 135,92,137,139,141,143,145,147,149,94,125,151,153,155,128,157,118,90,120,91,102,123,93,110,95, 127,96,97,130,98,132,99,134,100,136,101,138,103,140,104,142,105,144,106,146,107,148,108,150,109, 152,112,154,113,156,114,158,116,199,201,203,205,207,209,211,213,215,217,219,221,223,225,227,229,231, 233,235,237,239,241,243,245,196,248,250,252,254,256,258,260,262,264,266,268,270,247,272,274,200,159, 202,160,204,161,206,162,208,163,210,164,212,165,214,166,216,167,218,168,220,169,222,170,224,171,226, 172,228,173,230,174,232,175,234,176,236,177,238,178,240,179,242,180,244,181,246,182,183,249,184,251, 185,253,186,255,187,257,188,259,189,261,190,263,191,265,192,267,193,269,194,271,195,273,197,275,198, 351,353,355,293,358,360,362,364,366,350,369,371,373,375,377,316,380,357,381,383,385,387,309,389,292, 391,311,394,395,397,399,401,403,388,405,393,303,407,409,411,379,329,414,297,416,418,419,421,423,425, 321,427,429,413,431,433,435,437,439,441,443,445,447,449,451,453,455,457,459,461,463,465,467,469,368, 352,276,354,277,356,278,279,359,280,361,281,363,282,365,283,367,284,285,370,286,372,287,374,288,376, 289,378,290,291,300,382,294,384,295,386,296,319,298,390,299,392,301,302,312,396,304,398,305,400,306, 402,307,404,308,406,310,408,313,410,314,412,315,317,415,318,417,320,326,420,322,422,323,424,324,426, 325,428,327,430,328,432,330,434,331,436,332,438,333,440,334,442,335,444,336,446,337,448,338,450,339, 452,340,454,341,456,342,458,343,460,344,462,345,464,346,466,347,468,348,470,349,575,486,578,580,582, 584,521,586,506,589,591,593,595,597,599,577,601,603,604,606,608,610,612,614,616,617,619,621,623,504, 626,628,630,625,513,588,633,635,636,638,640,495,632,642,644,544,647,550,650,652,534,654,656,658,547, 660,662,664,666,540,669,552,670,477,672,674,676,678,680,668,682,684,686,646,687,531,659,548,524,649, 688,556,565,691,693,532,695,697,699,701,703,705,707,709,690,545,488,711,508,713,715,717,543,719,576, 471,472,579,473,581,474,583,475,585,476,587,478,479,590,480,592,481,594,482,596,483,598,484,600,485, 602,487,567,605,489,607,490,609,491,611,492,613,493,615,494,512,618,496,620,497,622,498,624,499,500, 627,501,629,502,631,503,505,634,507,569,637,509,639,510,641,511,643,514,645,515,516,648,517,518,651, 519,653,520,655,522,657,523,549,525,661,526,663,527,665,528,667,529,530,546,671,533,673,535,675,536, 677,537,679,538,681,539,683,541,685,542,573,566,689,551,553,692,554,694,555,696,557,698,558,700,559, 702,560,704,561,706,562,708,563,710,564,712,568,714,570,716,571,718,572,720,574,745,839,787,841,843, 845,847,849,851,853,855,857,800,860,862,864,866,868,870,871,766,874,876,878,761,880,882,884,723,885, 887,756,771,891,893,889,895,897,820,900,721,809,903,905,907,873,909,814,911,912,890,914,916,917,919, 921,767,923,924,739,926,928,930,932,934,936,749,938,810,796,941,943,945,947,949,940,748,951,953,859, 955,957,959,961,963,965,967,778,902,939,773,969,971,910,973,975,977,979,981,899,829,983,769,985,987, 788,989,991,833,830,993,995,821,997,999,1001,1003,1005,840,722,842,724,844,725,846,726,848,727,850,728, 852,729,854,730,856,731,858,732,733,861,734,863,735,865,736,867,737,869,738,780,872,740,741,875,742, 877,743,879,744,881,746,883,747,797,886,750,888,751,752,753,892,754,894,755,896,757,898,758,759,901, 760,762,904,763,906,764,908,765,777,768,823,913,770,915,772,811,918,774,920,775,922,776,808,925,779, 927,781,929,782,931,783,933,784,935,785,937,786,826,789,790,942,791,944,792,946,793,948,794,950,795, 952,798,954,799,956,801,958,802,960,803,962,804,964,805,966,806,968,807,970,812,972,813,974,815,976, 816,978,817,980,818,982,819,984,822,986,824,988,825,990,827,992,828,994,831,996,832,998,834,1000,835, 1002,836,1004,837,1006,838,1129,1131,1133,1134,1023,1136,1137,1138,1140,1021,1143,1145,1147,1057,1142,1150,1135,1152,1028, 1154,1085,1031,1113,1157,1025,1158,1160,1128,1163,1046,1166,1167,1169,1064,1172,1173,1175,1177,1047,1165,1049,1053,1045,1086, 1181,1088,1179,1184,1186,1188,1149,1190,1192,1118,1109,1196,1080,1171,1119,1030,1200,1202,1204,1013,1205,1083,1037,1208,1210, 1212,1214,1069,1082,1198,1217,1216,1207,1219,1125,1180,1106,1183,1222,1012,1224,1226,1041,1228,1010,1230,1232,1234,1236,1237, 1239,1241,1243,1245,1247,1221,1249,1251,1195,1253,1255,1257,1156,1259,1261,1263,1099,1194,1199,1265,1009,1267,1269,1271,1027, 1273,1275,1162,1130,1007,1132,1008,1121,1095,1011,1090,1070,1139,1014,1141,1015,1016,1144,1017,1146,1018,1148,1019,1020,1151, 1022,1153,1024,1155,1026,1029,1066,1159,1032,1161,1033,1034,1164,1035,1036,1073,1168,1038,1170,1039,1040,1093,1174,1042,1176, 1043,1178,1044,1048,1050,1182,1051,1052,1185,1054,1187,1055,1189,1056,1191,1058,1193,1059,1060,1061,1197,1062,1063,1065,1201, 1067,1203,1068,1078,1206,1071,1072,1209,1074,1211,1075,1213,1076,1215,1077,1079,1218,1081,1220,1084,1087,1223,1089,1225,1091, 1227,1092,1229,1094,1231,1096,1233,1097,1235,1098,1117,1238,1100,1240,1101,1242,1102,1244,1103,1246,1104,1248,1105,1250,1107, 1252,1108,1254,1110,1256,1111,1258,1112,1260,1114,1262,1115,1264,1116,1266,1120,1268,1122,1270,1123,1272,1124,1274,1126,1276, 1127,1279,1288,1383,1384,1386,1388,1374,1390,1321,1393,1290,1330,1395,1307,1360,1397,1399,1311,1402,1404,1373,1314,1342,1408, 1410,1411,1413,1318,1354,1282,1287,1417,1419,1291,1401,1378,1363,1406,1324,1375,1424,1415,1425,1427,1392,1428,1430,1332,1431, 1432,1301,1434,1436,1278,1438,1315,1440,1335,1380,1442,1444,1371,1447,1340,1449,1407,1357,1317,1452,1454,1296,1320,1456,1458, 1459,1461,1325,1416,1463,1361,1451,1466,1468,1310,1465,1470,1422,1472,1474,1476,1478,1372,1481,1483,1446,1480,1405,1389,1423, 1323,1350,1421,1485,1334,1487,1489,1277,1385,1280,1387,1281,1306,1283,1391,1284,1285,1394,1286,1396,1289,1398,1292,1400,1293, 1294,1403,1295,1347,1297,1298,1299,1409,1300,1327,1412,1302,1414,1303,1304,1305,1418,1308,1420,1309,1312,1313,1316,1344,1426, 1319,1348,1429,1322,1376,1353,1433,1326,1435,1328,1437,1329,1439,1331,1441,1333,1443,1336,1445,1337,1338,1448,1339,1450,1341, 1343,1453,1345,1455,1346,1457,1349,1377,1460,1351,1462,1352,1464,1355,1356,1467,1358,1469,1359,1471,1362,1473,1364,1475,1365, 1477,1366,1479,1367,1368,1482,1369,1484,1370,1486,1379,1488,1381,1490,1382,1543,1544,1493,1545,1526,1494,1535,1548,1510,1549, 1492,1550,1552,1553,1555,1506,1509,1527,1523,1522,1531,1503,1498,1516,1560,1559,1519,1537,1562,1540,1491,1499,1507,1532,1530, 1546,1557,1518,1529,1565,1558,1564,1541,1500,1547,1567,1528,1569,1539,1563,1566,1571,1521,1501,1496,1495,1497,1513,1534,1551, 1502,1512,1554,1504,1556,1505,1508,1511,1514,1561,1515,1517,1520,1524,1525,1533,1568,1536,1570,1538,1572,1542,1582,1589,1588, 1587,1580,1573,1586,1591,1574,1578,1576,1579,1592,1584,1583,1590,1581,1575,1577,1593,1585,1597,1595,1594,1596,1599,1600,1598] >; print "Group G is U3(4) < Sym(1600)";