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