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