/* www-ATLAS of Group Representations. U6(2) represented as permutations on 1408 points. */ G:=PermutationGroup<1408|\[ 1,4,3,2,9,11,12,8,5,15,6,7,19,21,10,16,23,26,13,20,14,32,17,34,36, 18,40,28,39,30,45,22,49,24,52,25,37,55,29,27,60,61,63,44,31,68,66,48,33,74, 51,35,72,54,38,83,85,87,82,41,42,94,43,97,98,47,100,46,104,105,107,53,110,50,114, 76,77,113,119,92,122,59,56,84,57,129,58,132,89,135,131,80,93,62,127,143,64,65,149,67, 153,151,156,69,70,162,71,165,142,73,167,152,78,75,172,173,174,176,79,179,141,81,181,124,125, 180,95,186,86,190,91,88,195,134,90,136,198,138,201,203,121,109,96,209,207,212,214,148,99,219, 102,112,101,224,155,103,227,225,229,231,218,106,163,237,108,241,111,168,222,243,221,115,116,117,251, 118,254,255,120,126,123,260,261,262,264,128,268,266,189,130,273,275,277,272,133,196,197,137,285,286, 139,289,140,291,293,295,145,297,144,299,300,146,213,147,305,307,309,161,150,220,171,169,317,154,158, 320,157,324,159,327,160,232,233,333,330,336,164,238,338,342,166,242,170,349,350,323,247,354,356,250, 175,347,362,177,178,367,366,370,371,182,183,184,306,185,381,188,383,187,386,388,390,194,191,395,192, 398,193,401,403,280,400,407,396,409,199,200,287,415,202,419,204,292,205,423,206,426,208,429,210,211, 301,302,436,437,215,263,216,443,217,445,311,365,444,448,315,431,223,451,453,226,457,455,246,228,348, 463,230,467,329,235,331,470,234,334,472,236,474,239,339,340,476,240,343,344,425,482,252,325,244,245, 486,487,488,248,491,249,357,496,498,494,361,253,363,504,312,257,256,368,509,258,259,515,516,514,375, 520,439,378,511,525,265,529,267,460,531,269,489,270,538,271,391,518,543,540,274,283,549,276,553,281, 278,558,279,560,497,562,282,524,284,569,567,412,572,414,288,573,574,577,290,580,461,582,294,462,345, 296,588,589,298,593,316,595,433,587,598,303,304,438,377,600,441,605,308,313,310,608,610,314,614,615, 318,619,319,621,322,623,321,627,628,384,421,424,326,464,631,634,328,637,639,332,471,335,644,337,646, 341,650,478,652,653,654,346,492,484,657,351,352,353,387,664,355,483,493,360,495,358,405,359,499,672, 674,502,503,364,677,679,507,682,369,510,379,685,687,374,372,373,691,392,519,376,694,696,698,408,380, 638,701,607,382,530,385,709,533,662,707,536,714,389,539,394,541,718,393,721,723,725,720,684,397,550, 729,733,399,737,602,740,736,402,745,404,749,406,673,752,565,755,411,757,410,760,761,413,416,417,763, 764,418,766,768,420,772,422,774,661,776,778,434,427,428,590,783,786,430,790,432,596,712,435,599,440, 601,555,796,604,442,800,528,446,609,447,611,612,613,449,450,810,809,811,452,815,454,818,456,822,820, 825,458,459,831,832,465,632,633,466,837,835,468,526,469,836,641,642,841,473,845,475,848,849,847,477, 852,479,480,481,655,667,485,658,803,859,584,534,663,490,665,865,656,868,870,670,710,500,563,501,875, 676,505,879,506,882,794,508,880,548,512,885,513,876,887,889,517,893,894,521,695,522,900,523,903,904, 527,906,908,909,911,706,535,708,532,671,916,597,919,537,923,921,926,542,929,547,544,722,545,724,546, 726,727,939,551,730,731,941,552,944,946,557,554,950,899,556,952,742,955,930,559,960,958,962,561,795, 873,564,964,754,566,867,568,970,973,570,571,891,575,576,910,578,981,579,769,984,983,581,986,583,985, 585,777,586,779,914,995,992,591,784,998,592,1002,1000,1005,594,1008,1009,793,681,750,603,1013,798,838,606, 1016,878,659,804,1020,1021,1022,1007,617,616,618,1026,1024,1027,620,1030,1029,622,1034,625,839,624,1038,866,626, 1042,1040,1045,1047,1033,629,630,833,1051,636,640,635,799,821,840,643,953,1018,1057,645,1058,649,647,648,1062, 851,651,922,854,989,1069,1071,858,660,860,1055,862,1075,864,666,824,756,668,1035,669,1082,1080,751,874,675, 688,1087,802,678,683,1093,680,883,1097,686,1100,689,1103,690,1106,762,1105,692,693,1112,1111,897,1114,739,697, 901,1119,699,700,1125,702,1128,703,704,765,705,1133,1134,780,915,711,1043,1137,713,1139,716,853,715,1116,1142, 717,1063,928,719,744,931,932,1147,1143,935,936,937,938,728,1151,732,942,1154,734,945,735,947,948,1158,738, 1088,741,842,954,743,1163,1165,747,1168,746,1171,748,1162,753,965,1175,1176,1124,1178,758,1161,972,759,1001,1155, 1184,1079,1186,1130,1189,767,982,771,770,775,773,1193,1195,855,990,991,782,993,1199,781,1201,997,785,999,788, 974,787,1003,1004,789,1006,808,791,792,1209,1011,1212,797,1213,1215,801,1216,843,1217,805,806,807,1221,813,1222, 812,814,1028,817,816,1039,1086,830,819,869,1053,1156,823,1031,827,1113,826,917,1235,828,1046,829,1238,1239,1214, 834,1052,1036,1054,861,1182,844,846,1237,1060,1244,850,927,1207,1065,1066,1141,1246,856,1172,857,1251,1073,1136,863, 1252,1077,1225,977,872,1233,871,1083,1224,1085,1032,877,951,1259,1261,1257,1196,881,1094,1265,1267,884,1270,1269,886, 1272,1274,888,1197,892,890,1276,1243,1109,1110,896,895,1041,898,1123,924,1279,1227,902,1120,1281,1284,1115,968,905, 1167,1288,907,1129,979,1287,1292,912,913,1296,1074,918,1145,920,1300,1067,925,934,1205,1138,1304,933,1230,1294,1150, 940,1152,1309,943,975,1037,1157,949,1159,1311,971,963,956,1164,957,1166,1126,959,1169,1250,961,1070,1268,1313,966, 967,1200,969,1179,1180,1181,1056,1323,976,1325,978,1187,1328,980,1329,1191,1192,987,1194,988,1092,1104,1198,994,1177, 996,1202,1203,1204,1144,1206,1064,1297,1010,1336,1334,1012,1014,1050,1015,1017,1019,1340,1219,1337,1023,1025,1342,1084,1078, 1256,1118,1303,1306,1148,1346,1347,1081,1298,1044,1236,1059,1048,1049,1339,1349,1242,1108,1061,1320,1068,1305,1318,1249,1170, 1072,1076,1253,1354,1255,1226,1091,1258,1089,1260,1090,1262,1263,1358,1095,1266,1096,1173,1099,1098,1359,1101,1273,1102,1286, 1107,1277,1362,1117,1280,1121,1282,1283,1122,1285,1275,1131,1127,1345,1290,1367,1132,1368,1149,1295,1135,1208,1234,1372,1140, 1310,1302,1228,1146,1247,1229,1350,1357,1153,1301,1160,1312,1174,1314,1315,1316,1317,1248,1319,1245,1379,1322,1183,1324,1185, 1326,1327,1188,1190,1343,1331,1332,1333,1211,1335,1210,1220,1338,1240,1218,1385,1223,1330,1361,1289,1231,1232,1370,1241,1307, 1351,1376,1353,1254,1355,1384,1308,1264,1271,1360,1344,1278,1363,1364,1365,1366,1291,1293,1369,1348,1371,1299,1373,1378,1375, 1352,1403,1374,1321,1380,1381,1395,1389,1356,1341,1386,1387,1396,1383,1390,1391,1392,1393,1394,1382,1388,1405,1398,1399,1400, 1401,1402,1377,1404,1397,1406,1407,1408] ,\[ 2,5,1,7,10,3,13,4,6,9,16,18,20,8,12,24,11,27,28,22,30,14,15,35,17, 38,41,42,19,44,21,47,23,50,37,53,25,56,26,58,33,62,29,65,66,31,70,32,72,75, 34,77,79,36,81,84,39,88,40,90,92,64,95,43,69,99,45,102,46,106,48,109,49,112,115, 51,117,52,120,54,123,55,125,86,127,57,130,133,59,136,60,138,61,140,142,63,145,147,150,151, 67,155,68,158,160,108,163,71,166,135,73,169,74,157,116,76,175,78,178,121,80,110,182,82,184, 83,119,85,188,191,87,193,134,89,196,197,91,200,93,204,94,206,207,96,211,97,215,98,217,154, 220,100,222,101,171,225,103,228,104,232,105,234,236,107,239,168,181,111,209,113,114,245,247,249,177, 252,118,224,256,122,259,183,124,263,126,266,128,269,129,271,274,131,278,132,280,282,199,283,137,202, 287,139,290,292,141,210,296,143,244,144,301,203,146,304,306,148,310,149,312,314,152,316,153,187,319, 156,322,325,214,159,329,331,161,334,162,337,338,164,341,165,344,167,347,170,351,172,353,173,357,174, 359,361,176,335,365,368,179,180,372,373,375,377,265,379,185,382,186,385,387,189,391,190,393,276,396, 192,399,402,194,405,195,258,408,198,411,413,336,201,417,420,311,294,367,205,424,427,349,208,431,433, 303,212,213,438,439,308,441,216,352,421,218,446,219,315,221,449,268,223,454,455,226,459,227,461,328, 229,465,230,468,231,332,233,471,364,235,473,340,475,237,238,477,333,240,480,241,242,484,243,467,485, 444,246,489,350,248,493,495,250,499,251,501,472,253,254,505,255,507,508,257,511,513,483,517,260,519, 261,522,262,524,264,527,530,531,267,533,534,389,536,270,539,541,272,544,273,546,548,275,551,554,277, 556,404,514,279,561,281,564,566,567,284,571,285,573,286,574,288,576,289,579,581,291,293,584,453,295, 586,430,297,591,298,594,299,509,300,302,599,339,601,602,305,604,307,481,309,348,609,313,612,452,317, 617,318,620,458,622,320,625,321,629,323,419,324,631,326,633,327,636,638,330,641,436,643,575,412,647, 648,479,342,343,607,345,655,346,423,658,659,383,662,492,354,666,355,664,356,497,414,358,670,671,360, 503,362,363,498,678,366,681,510,683,369,684,370,688,371,538,690,415,374,692,516,376,697,378,700,701, 380,704,381,706,532,708,384,710,711,386,713,388,716,589,390,542,392,719,722,394,726,395,728,729,397, 732,398,735,738,400,741,401,743,403,747,563,750,406,753,407,570,756,409,758,410,650,686,762,518,416, 765,572,418,769,770,435,661,422,445,425,779,426,781,783,428,785,429,788,791,462,432,434,793,651,437, 464,795,440,798,654,442,443,730,611,803,447,805,448,807,809,450,751,451,813,777,816,819,820,456,824, 457,827,829,630,460,833,463,834,835,466,784,839,640,841,469,674,470,843,844,474,846,600,850,476,645, 478,596,853,855,856,482,858,860,861,486,487,863,488,865,490,866,491,494,496,871,673,872,500,874,502, 504,877,680,880,506,775,676,792,577,752,512,886,746,515,890,891,695,520,896,521,898,699,901,523,703, 905,525,526,910,528,913,529,773,817,616,917,535,920,921,537,925,540,764,930,543,932,724,934,545,936, 937,547,731,940,549,550,942,725,552,947,553,568,739,555,951,953,557,956,558,958,559,961,560,810,812, 562,894,965,565,967,969,970,972,569,975,849,669,885,979,767,939,578,982,595,632,580,985,582,987,583, 989,585,991,993,587,996,588,927,590,999,1000,592,1004,593,615,652,597,1010,598,797,830,603,801,605,837, 606,608,1018,610,772,613,1023,614,814,1008,1024,618,1007,619,1028,1031,621,1032,823,1035,623,1036,624,1039,1040, 626,1044,627,1048,628,1049,1029,771,838,1052,634,639,635,1053,637,1055,642,876,870,644,1059,646,1033,808,1063, 649,1065,1067,653,1009,1070,656,988,657,665,916,660,1076,663,869,1078,667,1080,668,749,883,1083,672,1056,1085, 675,1088,677,1090,1092,679,1095,682,685,1099,1101,687,689,1104,1107,1108,691,1109,1111,693,1113,694,1115,696,1117, 919,698,1121,1123,1126,836,702,821,1130,912,922,705,1135,707,709,1074,918,712,1138,924,1140,714,1141,715,981, 1143,717,718,1146,740,720,944,721,1026,723,1002,938,727,1150,1017,1152,945,733,1156,734,1157,1159,736,737,923, 931,1001,954,742,1162,1164,744,1167,745,1170,1172,955,748,1060,966,754,1177,755,949,1179,757,1181,1155,759,1183, 760,761,763,1188,766,888,1105,768,1192,806,1193,1073,774,1196,776,1093,778,994,780,1200,1202,782,1203,1003,1204, 786,973,787,1205,995,789,790,845,1208,1210,794,796,1214,799,800,1025,802,1100,804,984,1219,1220,977,1062,811, 1223,1022,1051,815,1225,1136,960,818,1147,1227,1228,822,1229,1043,1231,825,1233,826,831,1030,828,1237,1213,1046,832, 1212,1240,1241,840,1075,842,1243,1238,1112,847,848,998,1064,851,892,852,1245,854,1248,1072,1178,857,859,862,1015, 1077,864,1079,867,897,868,1187,1254,873,1255,875,952,1258,878,1262,879,1264,1265,881,1110,882,1269,884,1253,1218, 1273,887,1232,1191,889,914,895,1066,1268,893,1271,964,1081,908,1277,899,1280,900,1281,902,968,903,1285,904,1171, 1129,906,1289,907,1291,909,911,1294,1097,1106,915,1297,1283,1299,1293,1158,1133,1013,926,928,1305,929,933,935,1307, 1308,1310,941,1037,943,1306,1161,946,1160,948,950,1267,1312,1166,1304,957,1315,1250,959,1061,1318,1174,962,963,997, 1201,1122,1320,1321,971,1182,974,1324,1176,976,1057,978,1303,1103,980,983,1331,1295,986,1021,1270,990,992,1276,1184, 1206,1175,1016,1257,1207,1005,1006,1014,1334,1211,1011,1050,1012,1239,1222,1084,1338,1019,1020,1252,1153,1342,1292,1027,1309, 1034,1114,1139,1344,1038,1189,1041,1118,1042,1047,1045,1131,1348,1302,1127,1242,1054,1335,1058,1247,1249,1068,1351,1069,1071, 1244,1353,1082,1216,1355,1086,1087,1260,1224,1089,1319,1354,1091,1266,1332,1094,1261,1096,1194,1296,1098,1360,1275,1347,1102, 1287,1278,1116,1363,1234,1274,1119,1120,1279,1364,1124,1125,1345,1361,1128,1235,1149,1132,1369,1134,1197,1370,1137,1154,1341, 1142,1144,1145,1374,1343,1148,1330,1236,1151,1300,1375,1311,1163,1165,1317,1168,1169,1333,1173,1378,1322,1180,1380,1326,1284, 1185,1186,1349,1383,1190,1195,1198,1199,1327,1209,1336,1215,1386,1217,1288,1221,1388,1226,1340,1230,1389,1359,1390,1391,1246, 1392,1251,1259,1357,1356,1256,1263,1282,1358,1366,1272,1372,1394,1365,1286,1290,1346,1396,1398,1399,1298,1323,1301,1401,1402, 1313,1314,1316,1381,1403,1325,1328,1382,1329,1337,1406,1339,1405,1397,1352,1384,1350,1362,1379,1367,1395,1368,1373,1400,1371, 1404,1376,1408,1377,1385,1407,1387,1393] >; print "Group G is U6(2) < Sym(1408)";