/* www-ATLAS of Group Representations. U6(2) represented as permutations on 2816 points. */ G:=PermutationGroup<2816|\[ 2,1,7,6,10,4,3,15,17,5,18,22,23,20,8,26,9,11,29,14,32,12,13,36,38, 16,33,42,19,45,47,21,27,40,51,24,46,25,57,34,59,28,62,64,30,37,31,70,71,73, 35,77,66,76,68,82,39,86,41,90,91,43,74,44,96,53,95,55,100,48,49,106,50,63,109, 54,52,114,115,117,99,56,122,120,103,58,128,129,105,60,61,134,108,138,67,65,143,145,81,69, 150,148,85,154,89,72,126,93,75,163,165,167,162,78,79,174,80,177,178,84,180,83,184,185,187, 107,190,87,88,196,156,157,195,92,202,204,206,94,210,212,214,209,97,218,98,221,222,102,224,101, 228,229,231,104,235,131,132,234,240,172,243,113,110,211,111,250,112,253,216,256,252,160,217,116,248, 264,118,119,270,121,274,272,277,123,124,283,125,286,263,127,290,288,293,295,133,130,299,300,301,303, 305,135,307,136,311,137,313,289,142,139,164,140,319,141,321,169,173,144,310,326,146,147,332,149,335, 334,338,151,152,344,153,347,273,158,155,351,352,353,355,159,358,262,161,360,315,316,359,175,365,166, 369,171,168,374,323,170,292,377,312,380,382,242,189,176,388,386,391,393,331,179,398,182,233,181,403, 337,183,406,404,408,410,397,186,345,416,188,420,192,208,191,308,257,193,427,194,430,432,429,197,198, 199,440,200,443,201,445,203,291,447,219,205,259,207,423,245,246,422,457,213,461,215,465,255,466,468, 220,431,470,474,476,269,223,481,226,225,448,276,227,486,484,488,490,480,230,284,496,232,401,500,400, 236,237,238,508,239,511,512,241,247,244,517,518,519,521,249,525,523,460,251,530,532,534,529,254,421, 425,258,542,543,260,546,261,548,550,552,266,554,265,556,557,267,475,268,562,564,566,282,271,482,350, 348,574,275,279,577,278,581,280,584,281,491,492,590,587,593,285,497,595,599,287,375,317,314,446,376, 607,294,611,298,296,327,297,616,617,580,504,621,623,507,302,614,629,304,632,306,424,309,336,638,637, 641,642,644,645,646,648,318,652,650,368,320,657,659,656,322,324,666,325,668,328,671,673,674,329,392, 330,679,681,683,343,333,399,689,340,692,339,696,341,699,342,411,412,705,702,708,346,417,710,714,349, 718,719,695,436,723,725,439,354,716,731,356,357,736,735,739,740,361,362,363,563,364,750,367,752,366, 755,757,759,373,370,764,371,767,372,770,772,662,769,776,765,778,378,379,664,784,381,788,383,669,384, 792,385,795,387,798,389,390,675,676,805,806,394,520,395,812,396,814,685,734,813,818,612,800,402,821, 823,405,827,825,435,407,615,833,409,837,701,414,703,840,413,706,842,415,844,418,711,712,846,419,715, 633,794,852,853,854,856,426,860,858,862,428,572,866,441,582,433,434,870,871,872,437,875,438,726,880, 882,878,730,442,732,888,444,601,890,893,686,450,449,737,899,451,452,904,453,454,455,680,456,913,459, 915,458,918,920,922,464,462,927,463,930,932,537,929,544,936,467,940,469,549,942,471,945,472,473,558, 559,951,952,477,647,478,958,479,960,568,636,959,963,483,965,967,485,971,969,503,487,717,977,489,981, 586,494,588,984,493,591,986,495,988,498,596,597,990,499,600,509,697,501,502,996,997,998,505,1001,506, 624,1006,1008,1004,628,510,630,1014,569,514,513,639,1019,515,516,1025,1026,1024,907,1030,808,910,1021,1035,522, 1039,524,974,1041,526,873,527,1048,528,923,1028,1053,1050,531,540,1059,533,1063,538,535,1068,536,1070,881,1072, 539,1034,541,1079,1077,865,1082,902,545,1083,1084,1088,547,1091,975,1093,551,832,602,553,1099,1100,555,1104,573, 1106,948,1098,1109,560,561,953,746,1111,956,1116,565,570,567,831,1119,1121,571,1125,1126,575,1130,576,1132,579, 1134,578,1138,1139,916,815,793,583,978,1142,1145,585,1148,1150,589,985,592,1155,594,1157,598,1161,992,1163,1164, 1166,603,604,605,1173,606,1002,609,1177,608,1181,610,1185,1183,781,613,1189,994,1190,618,619,620,756,1197,622, 894,1003,627,1005,625,774,626,1009,1205,1207,1012,1013,631,976,634,1211,1212,635,876,1215,1217,1017,1220,640,1020, 1222,783,1224,643,1227,1172,744,1230,954,747,1169,1234,649,1238,651,830,1240,653,999,654,1247,655,760,1228,1252, 1249,658,1257,663,660,1262,661,1264,1007,1266,665,1223,1268,1271,667,1274,670,1278,1279,672,1283,1284,802,1277,1287, 677,678,807,909,1289,810,1294,682,687,684,1296,1298,688,1302,690,1306,691,1308,694,1310,693,1314,1315,753,790, 889,698,834,1318,1321,700,1324,1326,704,841,707,1331,709,1333,713,1337,848,1339,868,1340,720,721,722,919,1347, 724,857,877,729,879,727,934,728,883,1355,1357,886,887,733,1360,1362,897,1365,738,900,748,1368,1370,743,741, 742,1374,761,1229,745,1377,1379,1381,777,749,1149,1384,1118,751,1239,754,1392,1242,1195,1390,1245,1397,758,1248,763, 1250,1401,762,1404,1406,1408,1403,1367,766,1178,1412,1416,768,1420,1291,1423,1419,771,1428,773,1432,775,1206,1435,1168, 1438,780,1440,779,1444,1445,782,785,786,1447,1448,1449,787,1451,1453,789,1457,791,1459,1194,1461,1463,803,796,797, 1280,1468,1471,799,1475,801,1285,1395,804,1288,809,1290,1259,1482,1293,811,1486,1038,816,1297,817,1299,1300,1301,819, 820,1496,1495,1498,822,1502,824,1505,826,1509,1507,1512,828,829,1518,1519,835,1319,1320,836,1524,1522,838,1036,839, 1523,1328,1329,1529,843,1533,845,1536,1537,1535,847,1540,849,850,1237,851,1544,1075,911,1548,1550,906,855,1213,1350, 1547,859,1060,1556,1560,861,1563,864,1565,863,1568,1569,1570,867,869,1341,1489,1575,1095,1044,1346,874,1348,1581,1214, 1584,1586,1353,1589,884,1073,885,1593,1359,1595,891,892,1174,1200,895,1604,896,1607,1608,898,1605,901,937,903,1612, 1344,905,924,1029,908,1616,1618,1620,912,1325,1622,1165,914,1040,917,1630,1043,1345,1628,1046,1634,921,1049,926,1051, 1638,925,1641,1643,1645,1640,928,1441,1113,1652,1649,931,1657,933,1661,935,1356,938,1663,1664,939,1666,1668,941,1671, 1672,949,943,944,1101,1677,1679,946,947,1107,1632,950,1110,955,1112,1065,1686,1115,957,1690,961,1120,962,1122,1123, 1124,964,1698,1697,1699,966,1703,968,1706,970,1710,1708,1713,972,973,1719,1720,979,1143,1144,980,1725,1723,982,1235, 983,1724,1152,1153,1729,987,1733,989,1736,1737,1735,991,1740,993,995,1191,1693,1742,1226,1243,1196,1000,1198,1748,1175, 1751,1753,1203,1393,1010,1267,1011,1758,1209,1015,1762,1016,1765,1480,1018,1763,1058,1022,1768,1023,1594,1770,1772,1027,1776, 1777,1031,1617,1032,1783,1033,1786,1787,1037,1789,1791,1792,1794,1627,1045,1629,1042,1354,1799,1108,1802,1047,1806,1804,1809, 1052,1812,1057,1054,1642,1055,1644,1056,1646,1647,1822,1061,1557,1558,1824,1062,1827,1829,1067,1064,1833,1834,1066,1837,1654, 1840,1836,1069,1845,1843,1847,1071,1685,1591,1074,1849,1546,1076,1750,1078,1258,1855,1859,1080,1081,1864,1085,1086,1087,1793, 1089,1869,1090,1477,1872,1871,1092,1874,1094,1873,1096,1596,1097,1673,1797,1883,1880,1102,1526,1887,1103,1891,1889,1894,1105, 1897,1454,1898,1684,1364,1662,1114,1902,1688,1525,1117,1905,1761,1192,1694,1909,1910,1912,1896,1128,1127,1756,1129,1916,1914, 1917,1131,1920,1919,1133,1924,1136,1727,1135,1929,1582,1137,1933,1931,1936,1938,1923,1140,1141,1721,1943,1147,1151,1146,1485, 1469,1709,1728,1154,1948,1907,1950,1156,1951,1160,1158,1159,1955,1739,1162,1805,1598,1877,1167,1964,1437,1176,1170,1968,1171, 1759,1970,1972,1974,1976,1179,1413,1414,1978,1180,1981,1983,1182,1583,1184,1987,1990,1186,1187,1188,1996,1997,1995,1741,1193, 1743,1947,1745,2002,1747,1199,1511,1564,1201,1925,1202,1774,2009,1204,2007,1434,1757,1208,1371,1210,1462,2017,1542,2015,2020, 2022,2024,1692,1216,1221,2030,1218,1219,1911,1766,2035,1225,2037,2039,1963,1231,1378,1232,2044,1233,2047,1236,2049,1926,2051, 2053,1389,1244,1391,1241,2058,1286,2061,1246,2064,2063,2067,1251,2069,1256,1253,1405,1254,1407,1255,1409,1410,2078,1261,2081, 1782,1260,2083,1425,2085,1813,1263,2090,2088,2092,1265,1481,1269,1270,2052,1272,2097,1273,2100,2099,1275,1276,1464,2056,2105, 2102,1281,2108,1282,2112,2110,2115,1962,1479,1433,1292,2119,1484,1726,1295,2122,1603,1342,1490,2126,2127,1304,1303,1305,2130, 2128,2131,1307,2134,2133,1309,2138,1312,1527,1311,2142,1749,1313,2146,2144,2148,2150,2137,1316,1317,1520,2154,1323,1327,1322, 1689,1508,1528,1330,1838,2124,2159,1332,2160,1336,1334,1335,2164,1539,1338,1574,1343,1576,2158,1578,2171,1580,1349,1712,1439, 1351,2139,1352,2178,2176,1497,1592,1358,1551,2183,1488,1361,1366,2189,1363,1610,2193,1369,2196,1372,2199,1373,2202,1587,2201, 1375,1376,2208,2207,2042,2210,1651,1380,2045,2215,1382,1383,2221,1385,2224,1386,1387,1450,1388,2229,2230,1465,2057,1394,1934, 2234,1396,2236,1399,1541,1398,2239,2240,1400,2165,2068,1402,1656,2070,2071,2245,2241,2074,2075,2076,2077,1411,2249,1415,1979, 2252,1417,1982,1418,2079,2080,2256,1421,1422,2025,1427,1424,1730,2084,1426,2261,2263,1430,2266,1429,2269,1431,2260,1436,1965, 2273,2274,2220,2276,1442,2278,2280,1989,1443,1890,2282,2285,2175,1446,2288,2289,2226,2292,1452,2098,1456,1455,1460,1458,2296, 2298,1543,2016,2101,1467,2103,2302,1466,2304,2107,1956,1470,2109,1473,1860,1472,2113,2114,1474,2116,1494,1476,1478,2313,2034, 2316,1483,2317,2320,1487,2321,1531,2322,1491,1492,1609,1493,2328,1500,2329,1499,1501,2132,1504,1503,1930,2182,1517,1506,1585, 1624,2156,2339,1510,1921,1514,2344,1513,1800,2348,1515,2149,1516,2352,2353,2351,2318,1521,2155,2140,2157,1577,1530,2283,1532, 1534,2350,2162,2358,1538,1886,2311,2167,2168,2238,2362,1683,1615,1545,1850,2306,2366,1549,2369,1552,2372,1553,2375,1554,2377, 1555,2379,1559,1825,2340,1561,1828,1562,2384,2383,2387,1566,2259,1858,1567,2111,2253,2393,2006,1573,1571,1572,2396,2326,2169, 2333,1579,2397,2173,2332,1994,1590,2346,1588,2179,2400,2391,2181,2136,1599,1878,1597,2406,2408,1600,2270,1601,2413,1602,1835, 2416,2418,2414,2404,1606,2190,2422,2425,1900,1611,2428,1613,2232,1614,2359,2365,1780,2337,1619,1784,2436,1621,2439,1623,2442, 1625,1665,1626,2447,2448,1674,1798,1631,2147,2450,1633,2452,1636,1635,2212,2454,1637,1811,1639,1814,1815,2334,2319,1818,1819, 1820,1821,1648,1830,1831,1650,2184,1653,1839,1655,2464,2466,1659,2469,1658,2471,1660,2463,2474,2444,2477,1667,1870,1670,1669, 1879,1676,1881,2482,1675,2484,1885,1678,1888,1681,1991,1680,1892,1893,1682,1895,2491,2493,1687,2494,2496,1691,2401,1731,2497, 1695,1696,1701,2499,1700,1702,1918,1705,1704,2143,2014,1718,1707,1752,1945,2254,1711,2135,1715,2209,1714,2059,1716,1937,1717, 2513,2514,2495,1722,1944,1927,1946,1744,1732,1734,2512,1953,2519,1738,1810,2490,1958,1959,2000,2233,1746,2520,2004,2501,1863, 1755,2509,1754,2010,2331,2013,1922,1760,2082,2527,2529,2525,2299,1764,2031,2533,2535,1767,2538,2537,1769,2540,2542,1771,2405, 1775,1773,2544,2518,2432,2424,1779,1778,2145,1781,2219,2065,2547,2503,1785,2437,2549,2552,2211,1853,1788,2468,2556,1790,2443, 1867,2555,2560,1795,1796,2564,2038,2170,1801,2243,1803,2568,1960,1807,1808,1817,2488,2235,2574,1816,2506,2562,2378,1823,2380, 2579,1826,1992,2141,2460,1832,2461,2582,1988,1848,1841,2465,1842,2467,2440,1844,2470,2412,1846,2021,2426,2584,1851,1852,2303, 1854,2388,1856,2389,1857,2390,1861,1949,2595,1862,2597,2357,1865,1866,2475,2600,1868,2602,2479,2480,1875,2429,1876,2188,2430, 2481,1882,2275,1884,2485,1966,2486,2487,2455,2489,1957,2565,1899,2611,2609,1901,1903,1942,2073,1904,1906,1908,2615,2325,2324, 1999,2616,1913,1915,2618,2180,2005,2001,2072,2524,2435,2043,2601,1928,1980,2576,2458,2625,1932,2626,2008,2566,1935,2511,1952, 1941,1939,1940,2614,2632,2517,2287,1954,2040,2376,2634,1961,2636,2637,2041,1967,2640,2639,1969,2641,2643,1971,2645,2411,1973, 2360,1975,2248,1977,2250,2620,2433,1985,1984,2483,2652,1986,2277,2279,2281,2012,2655,1993,2657,2612,1998,2003,2521,2661,2011, 2123,2523,2502,2029,2200,2018,2592,2019,2575,2590,2374,2268,2023,2028,2526,2026,2528,2027,2530,2531,2669,2032,2534,2206,2033, 2271,2670,2036,2297,2300,2607,2205,2382,2673,2336,2046,2216,2676,2048,2265,2678,2050,2225,2095,2677,2619,2054,2055,2664,2060, 2456,2062,2683,2066,2309,2451,2585,2342,2681,2255,2257,2685,2093,2086,2262,2087,2264,2222,2089,2267,2091,2536,2687,2094,2290, 2694,2096,2695,2294,2295,2301,2104,2385,2106,2305,2307,2308,2242,2310,2166,2117,2699,2118,2120,2153,2121,2125,2702,2129,2703, 2174,2403,2214,2573,2581,2246,2707,2708,2177,2682,2349,2161,2151,2152,2701,2710,2356,2204,2163,2172,2398,2712,2402,2335,2187, 2415,2185,2417,2186,2419,2420,2716,2191,2423,2192,2472,2195,2194,2717,2197,2642,2198,2651,2203,2672,2720,2213,2627,2217,2674, 2675,2218,2650,2644,2227,2223,2624,2680,2726,2228,2727,2247,2671,2231,2312,2347,2731,2237,2732,2733,2580,2631,2504,2244,2409, 2341,2665,2715,2251,2571,2505,2258,2686,2272,2457,2688,2689,2690,2691,2410,2692,2407,2742,2654,2284,2656,2286,2658,2693,2291, 2338,2293,2704,2605,2604,2697,2431,2698,2315,2633,2314,2395,2700,2354,2323,2327,2752,2330,2446,2381,2696,2744,2719,2557,2343, 2345,2548,2668,2756,2729,2572,2355,2610,2361,2648,2363,2364,2755,2368,2367,2370,2541,2371,2554,2373,2666,2762,2635,2684,2553, 2543,2386,2765,2594,2392,2596,2394,2598,2749,2711,2399,2713,2748,2449,2577,2646,2737,2628,2421,2427,2563,2545,2434,2550,2551, 2438,2445,2441,2706,2558,2459,2510,2453,2649,2462,2583,2473,2586,2587,2588,2589,2591,2599,2476,2478,2621,2606,2608,2492,2613, 2515,2498,2500,2603,2724,2679,2507,2508,2760,2516,2660,2522,2662,2779,2578,2532,2539,2761,2623,2546,2770,2763,2764,2705,2771, 2559,2561,2772,2630,2773,2567,2569,2570,2774,2741,2775,2667,2740,2800,2738,2735,2593,2766,2622,2767,2787,2754,2663,2659,2780, 2781,2617,2793,2747,2638,2629,2769,2784,2768,2709,2718,2647,2722,2723,2653,2743,2745,2759,2757,2721,2725,2728,2730,2734,2736, 2802,2807,2783,2714,2750,2751,2788,2778,2758,2795,2810,2746,2782,2803,2796,2808,2811,2753,2806,2785,2790,2799,2809,2797,2739, 2812,2776,2789,2813,2814,2794,2777,2791,2798,2786,2792,2801,2804,2805,2816,2815] ,\[ 3,5,8,1,11,2,13,16,4,19,21,6,24,7,12,18,27,9,30,10,15,33,35,37,14, 29,41,17,44,46,20,23,49,22,52,53,39,55,25,26,60,32,28,65,66,48,68,31,72,34, 75,78,79,36,81,38,84,40,88,63,42,92,43,94,87,97,45,99,47,102,104,74,107,50,110, 51,112,61,116,54,119,120,56,124,57,126,58,130,59,132,134,136,62,139,64,141,144,67,147,148, 69,152,70,155,71,157,159,73,161,164,76,168,77,170,172,118,175,80,123,179,82,182,83,186,85, 189,86,192,194,197,89,199,90,201,91,205,93,208,211,95,215,96,206,146,219,98,151,223,100,226, 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1880,2607,2285,2310,2306,1885,1905,2525,2311,1894,1895,1903,2609,2315,1900,1942,1901,2353,1902,2329,2180,2613,1908,1909,2126, 1910,2520,2251,2618,2619,1917,2620,2057,2069,1924,2337,1926,2452,2576,1928,2623,1929,2292,2008,1932,2435,1933,2150,1936,2445, 1938,2630,2631,2223,2356,1946,2633,1951,1964,1954,2363,2374,1961,2120,2638,2639,1967,2521,2498,2642,1970,2345,2646,1972,2473, 1974,2358,2648,2628,2649,1978,2650,1983,2484,2438,1985,2634,2653,1988,2391,1991,2656,2384,1993,2397,2381,2660,2009,2401,2131, 2011,2662,2014,2640,2016,2280,2409,2411,2019,2666,2020,2022,2519,2024,2417,2400,2026,2591,2661,2028,2423,2606,2031,2039,2418, 2033,2034,2671,2035,2294,2040,2426,2672,2627,2044,2652,2046,2047,2269,2443,2049,2679,2050,2629,2051,2053,2681,2366,2202,2637, 2675,2622,2561,2229,2067,2068,2636,2072,2074,2278,2462,2080,2535,2686,2467,2574,2087,2689,2376,2089,2645,2092,2093,2159,2094, 2573,2199,2096,2099,2605,2102,2544,2393,2489,2273,2122,2414,2490,2115,2116,2670,2427,2153,2118,2514,2499,2700,2125,2703,2560, 2579,2138,2210,2236,2705,2142,2477,2145,2214,2146,2148,2227,2709,2572,2441,2517,2157,2610,2160,2711,2178,2321,2713,2182,2183, 2528,2331,2185,2692,2712,2187,2534,2697,2190,2529,2192,2297,2564,2194,2718,2543,2708,2198,2555,2546,2212,2721,2510,2643,2215, 2216,2547,2722,2220,2221,2624,2724,2224,2348,2247,2228,2728,2230,2300,2729,2234,2252,2617,2446,2239,2240,2242,2243,2735,2704, 2246,2603,2511,2249,2568,2458,2736,2582,2261,2738,2263,2589,2266,2267,2608,2271,2741,2594,2279,2743,2598,2552,2286,2289,2710, 2456,2747,2293,2326,2298,2301,2677,2302,2693,2313,2611,2320,2750,2322,2556,2496,2328,2753,2459,2379,2335,2340,2615,2342,2754, 2755,2347,2349,2351,2757,2455,2758,2491,2740,2362,2621,2760,2367,2429,2664,2761,2644,2626,2371,2698,2759,2377,2696,2683,2763, 2383,2542,2654,2389,2766,2658,2676,2394,2396,2416,2668,2663,2403,2405,2408,2768,2413,2420,2550,2599,2448,2570,2770,2436,2437, 2673,2439,2706,2719,2442,2772,2450,2659,2454,2775,2685,2464,2466,2691,2469,2470,2472,2474,2632,2778,2478,2481,2482,2699,2780, 2497,2678,2782,2502,2702,2506,2783,2717,2769,2784,2527,2715,2714,2524,2531,2674,2716,2771,2540,2744,2786,2723,2554,2641,2558, 2625,2788,2790,2791,2566,2655,2793,2731,2571,2797,2798,2584,2799,2586,2588,2690,2745,2802,2595,2597,2600,2777,2602,2612,2804, 2614,2616,2803,2794,2669,2707,2647,2748,2635,2808,2725,2687,2764,2651,2767,2800,2657,2665,2667,2810,2680,2796,2682,2684,2809, 2688,2694,2746,2695,2813,2701,2806,2789,2779,2720,2742,2726,2807,2727,2774,2792,2730,2787,2732,2733,2734,2812,2737,2801,2816, 2739,2815,2749,2805,2751,2752,2756,2811,2762,2765,2773,2776,2814,2781,2785,2795] >; print "Group G is U6(2) < Sym(2816)";