/*
www-ATLAS of Group Representations.
U6(2):2 represented as permutations on 1408 points.
*/

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