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