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