C₂×C₃₃₄₃⋊C₃ #34095385

order	20058
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₃₃₄₃⋊C₃
unambiguous semidirect product	(C₂×C₃₃₄₃)⋊C₃

Splittings

Fitting, socle, Hall	C₂×C₃₃₄₃ ⋊ C₃
derived, Sylow	C₃₃₄₃ ⋊ C₂×C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	C₃₃₄₃⋊C₃
commutator, cosocle, hypocenter	C₃₃₄₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₃₄₃	C₃
LCS	G ▷ C₃₃₄₃
UCS	C₁ ◁ C₂

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 3345
transitive degree	μ_t(G) = 6686

A minimal faithful permutation representation — 2 generators on 3345 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,782)(657,720,779)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,777,722)(716,780,719)(718,784,852)(721,787,849)(724,790,846)(727,793,843)(730,796,840)(733,799,837)(736,802,834)(739,805,831)(742,808,828)(745,811,825)(748,814,822)(751,817,819)(754,820,816)(757,823,813)(760,826,810)(763,829,807)(766,832,804)(769,835,801)(772,838,798)(775,841,795)(778,844,792)(781,847,789)(783,850,786)(785,854,925)(788,857,922)(791,860,919)(794,863,916)(797,866,913)(800,869,910)(803,872,907)(806,875,904)(809,878,901)(812,881,898)(815,884,895)(818,887,892)(821,890,889)(824,893,886)(827,896,883)(830,899,880)(833,902,877)(836,905,874)(839,908,871)(842,911,868)(845,914,865)(848,917,862)(851,920,859)(853,923,856)(855,927,1001)(858,930,998)(861,933,995)(864,936,992)(867,939,989)(870,942,986)(873,945,983)(876,948,980)(879,951,977)(882,954,974)(885,957,971)(888,960,968)(891,963,965)(894,966,962)(897,969,959)(900,972,956)(903,975,953)(906,978,950)(909,981,947)(912,984,944)(915,987,941)(918,990,938)(921,993,935)(924,996,932)(926,999,929)(928,1003,1080)(931,1006,1077)(934,1009,1074)(937,1012,1071)(940,1015,1068)(943,1018,1065)(946,1021,1062)(949,1024,1059)(952,1027,1056)(955,1030,1053)(958,1033,1050)(961,1036,1047)(964,1039,1044)(967,1042,1041)(970,1045,1038)(973,1048,1035)(976,1051,1032)(979,1054,1029)(982,1057,1026)(985,1060,1023)(988,1063,1020)(991,1066,1017)(994,1069,1014)(997,1072,1011)(1000,1075,1008)(1002,1078,1005)(1004,1082,1162)(1007,1085,1159)(1010,1088,1156)(1013,1091,1153)(1016,1094,1150)(1019,1097,1147)(1022,1100,1144)(1025,1103,1141)(1028,1106,1138)(1031,1109,1135)(1034,1112,1132)(1037,1115,1129)(1040,1118,1126)(1043,1121,1123)(1046,1124,1120)(1049,1127,1117)(1052,1130,1114)(1055,1133,1111)(1058,1136,1108)(1061,1139,1105)(1064,1142,1102)(1067,1145,1099)(1070,1148,1096)(1073,1151,1093)(1076,1154,1090)(1079,1157,1087)(1081,1160,1084)(1083,1164,1247)(1086,1167,1244)(1089,1170,1241)(1092,1173,1238)(1095,1176,1235)(1098,1179,1232)(1101,1182,1229)(1104,1185,1226)(1107,1188,1223)(1110,1191,1220)(1113,1194,1217)(1116,1197,1214)(1119,1200,1211)(1122,1203,1208)(1125,1206,1205)(1128,1209,1202)(1131,1212,1199)(1134,1215,1196)(1137,1218,1193)(1140,1221,1190)(1143,1224,1187)(1146,1227,1184)(1149,1230,1181)(1152,1233,1178)(1155,1236,1175)(1158,1239,1172)(1161,1242,1169)(1163,1245,1166)(1165,1249,1335)(1168,1252,1332)(1171,1255,1329)(1174,1258,1326)(1177,1261,1323)(1180,1264,1320)(1183,1267,1317)(1186,1270,1314)(1189,1273,1311)(1192,1276,1308)(1195,1279,1305)(1198,1282,1302)(1201,1285,1299)(1204,1288,1296)(1207,1291,1293)(1210,1294,1290)(1213,1297,1287)(1216,1300,1284)(1219,1303,1281)(1222,1306,1278)(1225,1309,1275)(1228,1312,1272)(1231,1315,1269)(1234,1318,1266)(1237,1321,1263)(1240,1324,1260)(1243,1327,1257)(1246,1330,1254)(1248,1333,1251)(1250,1337,1426)(1253,1340,1423)(1256,1343,1420)(1259,1346,1417)(1262,1349,1414)(1265,1352,1411)(1268,1355,1408)(1271,1358,1405)(1274,1361,1402)(1277,1364,1399)(1280,1367,1396)(1283,1370,1393)(1286,1373,1390)(1289,1376,1387)(1292,1379,1384)(1295,1382,1381)(1298,1385,1378)(1301,1388,1375)(1304,1391,1372)(1307,1394,1369)(1310,1397,1366)(1313,1400,1363)(1316,1403,1360)(1319,1406,1357)(1322,1409,1354)(1325,1412,1351)(1328,1415,1348)(1331,1418,1345)(1334,1421,1342)(1336,1424,1339)(1338,1428,1520)(1341,1431,1517)(1344,1434,1514)(1347,1437,1511)(1350,1440,1508)(1353,1443,1505)(1356,1446,1502)(1359,1449,1499)(1362,1452,1496)(1365,1455,1493)(1368,1458,1490)(1371,1461,1487)(1374,1464,1484)(1377,1467,1481)(1380,1470,1478)(1383,1473,1475)(1386,1476,1472)(1389,1479,1469)(1392,1482,1466)(1395,1485,1463)(1398,1488,1460)(1401,1491,1457)(1404,1494,1454)(1407,1497,1451)(1410,1500,1448)(1413,1503,1445)(1416,1506,1442)(1419,1509,1439)(1422,1512,1436)(1425,1515,1433)(1427,1518,1430)(1429,1522,1617)(1432,1525,1614)(1435,1528,1611)(1438,1531,1608)(1441,1534,1605)(1444,1537,1602)(1447,1540,1599)(1450,1543,1596)(1453,1546,1593)(1456,1549,1590)(1459,1552,1587)(1462,1555,1584)(1465,1558,1581)(1468,1561,1578)(1471,1564,1575)(1474,1567,1572)(1477,1570,1569)(1480,1573,1566)(1483,1576,1563)(1486,1579,1560)(1489,1582,1557)(1492,1585,1554)(1495,1588,1551)(1498,1591,1548)(1501,1594,1545)(1504,1597,1542)(1507,1600,1539)(1510,1603,1536)(1513,1606,1533)(1516,1609,1530)(1519,1612,1527)(1521,1615,1524)(1523,1619,1717)(1526,1622,1714)(1529,1625,1711)(1532,1628,1708)(1535,1631,1705)(1538,1634,1702)(1541,1637,1699)(1544,1640,1696)(1547,1643,1693)(1550,1646,1690)(1553,1649,1687)(1556,1652,1684)(1559,1655,1681)(1562,1658,1678)(1565,1661,1675)(1568,1664,1672)(1571,1667,1669)(1574,1670,1666)(1577,1673,1663)(1580,1676,1660)(1583,1679,1657)(1586,1682,1654)(1589,1685,1651)(1592,1688,1648)(1595,1691,1645)(1598,1694,1642)(1601,1697,1639)(1604,1700,1636)(1607,1703,1633)(1610,1706,1630)(1613,1709,1627)(1616,1712,1624)(1618,1715,1621)(1620,1719,1820)(1623,1722,1817)(1626,1725,1814)(1629,1728,1811)(1632,1731,1808)(1635,1734,1805)(1638,1737,1802)(1641,1740,1799)(1644,1743,1796)(1647,1746,1793)(1650,1749,1790)(1653,1752,1787)(1656,1755,1784)(1659,1758,1781)(1662,1761,1778)(1665,1764,1775)(1668,1767,1772)(1671,1770,1769)(1674,1773,1766)(1677,1776,1763)(1680,1779,1760)(1683,1782,1757)(1686,1785,1754)(1689,1788,1751)(1692,1791,1748)(1695,1794,1745)(1698,1797,1742)(1701,1800,1739)(1704,1803,1736)(1707,1806,1733)(1710,1809,1730)(1713,1812,1727)(1716,1815,1724)(1718,1818,1721)(1720,1822,1926)(1723,1825,1923)(1726,1828,1920)(1729,1831,1917)(1732,1834,1914)(1735,1837,1911)(1738,1840,1908)(1741,1843,1905)(1744,1846,1902)(1747,1849,1899)(1750,1852,1896)(1753,1855,1893)(1756,1858,1890)(1759,1861,1887)(1762,1864,1884)(1765,1867,1881)(1768,1870,1878)(1771,1873,1875)(1774,1876,1872)(1777,1879,1869)(1780,1882,1866)(1783,1885,1863)(1786,1888,1860)(1789,1891,1857)(1792,1894,1854)(1795,1897,1851)(1798,1900,1848)(1801,1903,1845)(1804,1906,1842)(1807,1909,1839)(1810,1912,1836)(1813,1915,1833)(1816,1918,1830)(1819,1921,1827)(1821,1924,1824)(1823,1928,2035)(1826,1931,2032)(1829,1934,2029)(1832,1937,2026)(1835,1940,2023)(1838,1943,2020)(1841,1946,2017)(1844,1949,2014)(1847,1952,2011)(1850,1955,2008)(1853,1958,2005)(1856,1961,2002)(1859,1964,1999)(1862,1967,1996)(1865,1970,1993)(1868,1973,1990)(1871,1976,1987)(1874,1979,1984)(1877,1982,1981)(1880,1985,1978)(1883,1988,1975)(1886,1991,1972)(1889,1994,1969)(1892,1997,1966)(1895,2000,1963)(1898,2003,1960)(1901,2006,1957)(1904,2009,1954)(1907,2012,1951)(1910,2015,1948)(1913,2018,1945)(1916,2021,1942)(1919,2024,1939)(1922,2027,1936)(1925,2030,1933)(1927,2033,1930)(1929,2037,2147)(1932,2040,2144)(1935,2043,2141)(1938,2046,2138)(1941,2049,2135)(1944,2052,2132)(1947,2055,2129)(1950,2058,2126)(1953,2061,2123)(1956,2064,2120)(1959,2067,2117)(1962,2070,2114)(1965,2073,2111)(1968,2076,2108)(1971,2079,2105)(1974,2082,2102)(1977,2085,2099)(1980,2088,2096)(1983,2091,2093)(1986,2094,2090)(1989,2097,2087)(1992,2100,2084)(1995,2103,2081)(1998,2106,2078)(2001,2109,2075)(2004,2112,2072)(2007,2115,2069)(2010,2118,2066)(2013,2121,2063)(2016,2124,2060)(2019,2127,2057)(2022,2130,2054)(2025,2133,2051)(2028,2136,2048)(2031,2139,2045)(2034,2142,2042)(2036,2145,2039)(2038,2149,2197)(2041,2151,2258)(2044,2154,2255)(2047,2157,2252)(2050,2160,2249)(2053,2163,2246)(2056,2166,2243)(2059,2169,2240)(2062,2172,2237)(2065,2175,2234)(2068,2178,2231)(2071,2181,2228)(2074,2184,2225)(2077,2187,2222)(2080,2190,2219)(2083,2193,2216)(2086,2196,2213)(2089,2199,2210)(2092,2202,2207)(2095,2205,2204)(2098,2208,2201)(2101,2211,2198)(2104,2214,2195)(2107,2217,2192)(2110,2220,2189)(2113,2223,2186)(2116,2226,2183)(2119,2229,2180)(2122,2232,2177)(2125,2235,2174)(2128,2238,2171)(2131,2241,2168)(2134,2244,2165)(2137,2247,2162)(2140,2250,2159)(2143,2253,2156)(2146,2256,2153)(2148,2259,2150)(2152,2263,2307)(2155,2265,2367)(2158,2268,2364)(2161,2271,2361)(2164,2274,2358)(2167,2277,2355)(2170,2280,2352)(2173,2283,2349)(2176,2286,2346)(2179,2289,2343)(2182,2292,2340)(2185,2295,2337)(2188,2298,2334)(2191,2301,2331)(2194,2304,2328)(2200,2309,2323)(2203,2312,2320)(2206,2315,2317)(2209,2318,2314)(2212,2321,2311)(2215,2324,2308)(2218,2326,2306)(2221,2329,2303)(2224,2332,2300)(2227,2335,2297)(2230,2338,2294)(2233,2341,2291)(2236,2344,2288)(2239,2347,2285)(2242,2350,2282)(2245,2353,2279)(2248,2356,2276)(2251,2359,2273)(2254,2362,2270)(2257,2365,2267)(2260,2368,2264)(2261,2310,2262)(2266,2372,2413)(2269,2374,2470)(2272,2377,2467)(2275,2380,2464)(2278,2383,2461)(2281,2386,2458)(2284,2389,2455)(2287,2392,2452)(2290,2395,2449)(2293,2398,2446)(2296,2401,2443)(2299,2404,2440)(2302,2407,2437)(2305,2410,2434)(2313,2416,2427)(2316,2419,2424)(2319,2422,2421)(2322,2425,2418)(2325,2428,2415)(2327,2430,2414)(2330,2432,2412)(2333,2435,2409)(2336,2438,2406)(2339,2441,2403)(2342,2444,2400)(2345,2447,2397)(2348,2450,2394)(2351,2453,2391)(2354,2456,2388)(2357,2459,2385)(2360,2462,2382)(2363,2465,2379)(2366,2468,2376)(2369,2471,2373)(2370,2417,2371)(2375,2475,2513)(2378,2477,2567)(2381,2480,2564)(2384,2483,2561)(2387,2486,2558)(2390,2489,2555)(2393,2492,2552)(2396,2495,2549)(2399,2498,2546)(2402,2501,2543)(2405,2504,2540)(2408,2507,2537)(2411,2510,2534)(2420,2517,2525)(2423,2520,2522)(2426,2523,2519)(2429,2526,2516)(2431,2528,2515)(2433,2530,2514)(2436,2532,2512)(2439,2535,2509)(2442,2538,2506)(2445,2541,2503)(2448,2544,2500)(2451,2547,2497)(2454,2550,2494)(2457,2553,2491)(2460,2556,2488)(2463,2559,2485)(2466,2562,2482)(2469,2565,2479)(2472,2568,2476)(2473,2518,2474)(2478,2572,2607)(2481,2574,2658)(2484,2577,2655)(2487,2580,2652)(2490,2583,2649)(2493,2586,2646)(2496,2589,2643)(2499,2592,2640)(2502,2595,2637)(2505,2598,2634)(2508,2601,2631)(2511,2604,2628)(2521,2612,2617)(2524,2615,2614)(2527,2618,2611)(2529,2620,2610)(2531,2622,2609)(2533,2624,2608)(2536,2626,2606)(2539,2629,2603)(2542,2632,2600)(2545,2635,2597)(2548,2638,2594)(2551,2641,2591)(2554,2644,2588)(2557,2647,2585)(2560,2650,2582)(2563,2653,2579)(2566,2656,2576)(2569,2659,2573)(2570,2613,2571)(2575,2663,2695)(2578,2665,2743)(2581,2668,2740)(2584,2671,2737)(2587,2674,2734)(2590,2677,2731)(2593,2680,2728)(2596,2683,2725)(2599,2686,2722)(2602,2689,2719)(2605,2692,2716)(2616,2701,2703)(2619,2704,2700)(2621,2706,2699)(2623,2708,2698)(2625,2710,2697)(2627,2712,2696)(2630,2714,2694)(2633,2717,2691)(2636,2720,2688)(2639,2723,2685)(2642,2726,2682)(2645,2729,2679)(2648,2732,2676)(2651,2735,2673)(2654,2738,2670)(2657,2741,2667)(2660,2744,2664)(2661,2702,2662)(2666,2748,2777)(2669,2750,2822)(2672,2753,2819)(2675,2756,2816)(2678,2759,2813)(2681,2762,2810)(2684,2765,2807)(2687,2768,2804)(2690,2771,2801)(2693,2774,2798)(2705,2784,2783)(2707,2786,2782)(2709,2788,2781)(2711,2790,2780)(2713,2792,2779)(2715,2794,2778)(2718,2796,2776)(2721,2799,2773)(2724,2802,2770)(2727,2805,2767)(2730,2808,2764)(2733,2811,2761)(2736,2814,2758)(2739,2817,2755)(2742,2820,2752)(2745,2823,2749)(2746,2785,2747)(2751,2827,2853)(2754,2829,2895)(2757,2832,2892)(2760,2835,2889)(2763,2838,2886)(2766,2841,2883)(2769,2844,2880)(2772,2847,2877)(2775,2850,2874)(2787,2860,2859)(2789,2862,2858)(2791,2864,2857)(2793,2866,2856)(2795,2868,2855)(2797,2870,2854)(2800,2872,2852)(2803,2875,2849)(2806,2878,2846)(2809,2881,2843)(2812,2884,2840)(2815,2887,2837)(2818,2890,2834)(2821,2893,2831)(2824,2896,2828)(2825,2861,2826)(2830,2900,2923)(2833,2902,2962)(2836,2905,2959)(2839,2908,2956)(2842,2911,2953)(2845,2914,2950)(2848,2917,2947)(2851,2920,2944)(2863,2930,2929)(2865,2932,2928)(2867,2934,2927)(2869,2936,2926)(2871,2938,2925)(2873,2940,2924)(2876,2942,2922)(2879,2945,2919)(2882,2948,2916)(2885,2951,2913)(2888,2954,2910)(2891,2957,2907)(2894,2960,2904)(2897,2963,2901)(2898,2931,2899)(2903,2967,2987)(2906,2969,3023)(2909,2972,3020)(2912,2975,3017)(2915,2978,3014)(2918,2981,3011)(2921,2984,3008)(2933,2994,2993)(2935,2996,2992)(2937,2998,2991)(2939,3000,2990)(2941,3002,2989)(2943,3004,2988)(2946,3006,2986)(2949,3009,2983)(2952,3012,2980)(2955,3015,2977)(2958,3018,2974)(2961,3021,2971)(2964,3024,2968)(2965,2995,2966)(2970,3028,3045)(2973,3030,3078)(2976,3033,3075)(2979,3036,3072)(2982,3039,3069)(2985,3042,3066)(2997,3052,3051)(2999,3054,3050)(3001,3056,3049)(3003,3058,3048)(3005,3060,3047)(3007,3062,3046)(3010,3064,3044)(3013,3067,3041)(3016,3070,3038)(3019,3073,3035)(3022,3076,3032)(3025,3079,3029)(3026,3053,3027)(3031,3083,3097)(3034,3085,3127)(3037,3088,3124)(3040,3091,3121)(3043,3094,3118)(3055,3104,3103)(3057,3106,3102)(3059,3108,3101)(3061,3110,3100)(3063,3112,3099)(3065,3114,3098)(3068,3116,3096)(3071,3119,3093)(3074,3122,3090)(3077,3125,3087)(3080,3128,3084)(3081,3105,3082)(3086,3132,3143)(3089,3134,3170)(3092,3137,3167)(3095,3140,3164)(3107,3150,3149)(3109,3152,3148)(3111,3154,3147)(3113,3156,3146)(3115,3158,3145)(3117,3160,3144)(3120,3162,3142)(3123,3165,3139)(3126,3168,3136)(3129,3171,3133)(3130,3151,3131)(3135,3175,3183)(3138,3177,3207)(3141,3180,3204)(3153,3190,3189)(3155,3192,3188)(3157,3194,3187)(3159,3196,3186)(3161,3198,3185)(3163,3200,3184)(3166,3202,3182)(3169,3205,3179)(3172,3208,3176)(3173,3191,3174)(3178,3212,3217)(3181,3214,3238)(3193,3224,3223)(3195,3226,3222)(3197,3228,3221)(3199,3230,3220)(3201,3232,3219)(3203,3234,3218)(3206,3236,3216)(3209,3239,3213)(3210,3225,3211)(3215,3243,3245)(3227,3252,3251)(3229,3254,3250)(3231,3256,3249)(3233,3258,3248)(3235,3260,3247)(3237,3262,3246)(3240,3264,3244)(3241,3253,3242)(3255,3274,3273)(3257,3276,3272)(3259,3278,3271)(3261,3280,3270)(3263,3282,3269)(3265,3284,3268)(3266,3275,3267)(3277,3293,3292)(3279,3295,3291)(3281,3297,3290)(3283,3299,3289)(3285,3301,3288)(3286,3294,3287)(3296,3309,3308)(3298,3311,3307)(3300,3313,3306)(3302,3315,3305)(3303,3310,3304)(3312,3322,3321)(3314,3324,3320)(3316,3326,3319)(3317,3323,3318)(3325,3332,3331)(3327,3334,3330)(3328,3333,3329)(3335,3339,3338)(3336,3340,3337)(3341,3343,3342)(3344,3345);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,654,718,785,855,928,1004,1083,1165,1250,1338,1429,1523,1620,1720,1823,1929,2038,2082,1864,1658,1464,1282,1112,954,808,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,876,949,1025,1104,1186,1271,1359,1450,1544,1641,1741,1844,1950,2059,2170,2281,2387,2487,2581,2669,2751,2774,2601,2404,2184,1961,1749,1549,1361,1185,1021,869,729,601,485,381,289,331,375,421,470,522,577,635,696,760,827,897,970,1046,1125,1207,1292,1380,1471,1565,1662,1762,1865,1971,2080,2191,2302,2408,2508,2602,2690,2772,2848,2918,2982,3040,3092,3138,3178,3180,3091,2978,2841,2680,2495,2286,2061,1843,1637,1443,1261,1091,933,787,653,716,781,848,918,991,1067,1146,1228,1313,1401,1492,1586,1683,1783,1886,1992,2101,2212,2322,2426,2524,2616,2702,2568,2365,2142,1924,1717,1817,1920,2026,2135,2246,2355,2458,2555,2646,2731,2810,2883,2950,3011,3066,3028,2902,2753,2580,2383,2163,1940,1728,1528,1340,1164,1248,1334,1422,1513,1607,1704,1804,1907,2013,2122,2233,2342,2445,2542,2633,2718,2797,2871,2939,3001,3057,3107,3151,3079,2960,2817,2650,2459,2244,2021,1809,1609,1421,1245,1080,1159,1241,1326,1414,1505,1599,1696,1796,1899,2005,2114,2225,2334,2437,2534,2475,2265,2040,1822,1927,2034,2143,2254,2363,2466,2563,2654,2739,2818,2891,2958,3019,3074,3123,3166,3203,3235,3261,3281,3298,3312,3323,3301,3262,3202,3119,3012,2881,2726,2547,2344,2121,1903,1697,1503,1321,1151,993,847,713,590,648,709,773,840,910,983,1059,1138,1220,1305,1393,1484,1578,1675,1775,1878,1984,2093,2204,2314,2418,2516,2610,2698,2780,2856,2926,2990,3048,3100,3146,3186,3220,3248,3270,3289,3305,3318,3309,3276,3228,3156,3060,2940,2796,2629,2438,2223,2000,1788,1588,1400,1224,1060,908,768,640,524,420,328,247,284,324,367,413,462,514,569,627,688,752,819,889,962,1038,1117,1199,1284,1372,1463,1557,1654,1754,1857,1963,2072,2183,2294,2400,2500,2594,2682,2764,2840,2910,2974,3032,3084,3131,3104,2996,2864,2708,2528,2324,2100,1882,1676,1482,1300,1130,972,826,692,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,868,941,1017,1096,1178,1263,1351,1442,1536,1633,1733,1836,1942,2051,2162,2273,2379,2479,2573,2662,2612,2419,2202,1979,1767,1567,1379,1203,1039,887,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,861,934,1010,1089,1171,1256,1344,1435,1529,1626,1726,1829,1935,2044,2155,2266,2304,2079,1861,1655,1461,1279,1109,951,805,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,745,812,882,955,1031,1110,1192,1277,1365,1456,1550,1647,1747,1850,1956,2065,2176,2287,2393,2493,2587,2675,2757,2833,2903,2920,2771,2598,2401,2181,1958,1746,1546,1358,1182,1018,866,726,598,482,378,426,476,528,583,641,702,766,833,903,976,1052,1131,1213,1298,1386,1477,1571,1668,1768,1871,1977,2086,2197,2307,2413,2513,2607,2695,2777,2853,2923,2987,3045,3097,3143,3183,3217,3245,3243,3177,3088,2975,2838,2677,2492,2283,2058,1840,1634,1440,1258,1088,930,784,853,924,997,1073,1152,1234,1319,1407,1498,1592,1689,1789,1892,1998,2107,2218,2327,2431,2529,2621,2707,2787,2861,2744,2565,2362,2139,1921,1715,1520,1614,1711,1811,1914,2020,2129,2240,2349,2452,2549,2640,2725,2804,2877,2944,2900,2750,2577,2380,2160,1937,1725,1525,1337,1427,1519,1613,1710,1810,1913,2019,2128,2239,2348,2451,2548,2639,2724,2803,2876,2943,3005,3061,3111,3155,3193,3225,3171,3076,2957,2814,2647,2456,2241,2018,1806,1606,1418,1242,1078,925,998,1074,1153,1235,1320,1408,1499,1593,1690,1790,1893,1999,2108,2219,2328,2263,2037,2148,2260,2369,2472,2569,2660,2745,2824,2897,2964,3025,3080,3129,3172,3209,3240,3265,3285,3302,3316,3327,3335,3340,3326,3299,3260,3200,3116,3009,2878,2723,2544,2341,2118,1900,1694,1500,1318,1148,990,844,710,588,477,529,584,642,703,767,834,904,977,1053,1132,1214,1299,1387,1478,1572,1669,1769,1872,1978,2087,2198,2308,2414,2514,2608,2696,2778,2854,2924,2988,3046,3098,3144,3184,3218,3246,3268,3287,3274,3226,3154,3058,2938,2794,2626,2435,2220,1997,1785,1585,1397,1221,1057,905,765,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,746,813,883,956,1032,1111,1193,1278,1366,1457,1551,1648,1748,1851,1957,2066,2177,2288,2394,2494,2588,2676,2758,2834,2904,2968,3027,2994,2862,2706,2526,2321,2097,1879,1673,1479,1297,1127,969,823,689,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,862,935,1011,1090,1172,1257,1345,1436,1530,1627,1727,1830,1936,2045,2156,2267,2373,2474,2416,2199,1976,1764,1564,1376,1200,1036,884,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,867,940,1016,1095,1177,1262,1350,1441,1535,1632,1732,1835,1941,2050,2161,2272,2378,2478,2510,2301,2076,1858,1652,1458,1276,1106,948,802,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,818,888,961,1037,1116,1198,1283,1371,1462,1556,1653,1753,1856,1962,2071,2182,2293,2399,2499,2593,2681,2763,2839,2909,2973,3031,3042,2917,2768,2595,2398,2178,1955,1743,1543,1355,1179,1015,863,723,595,479,533,589,647,708,772,839,909,982,1058,1137,1219,1304,1392,1483,1577,1674,1774,1877,1983,2092,2203,2313,2417,2259,2035,2144,2255,2364,2467,2564,2655,2740,2819,2892,2959,3020,3075,3124,3167,3204,3175,3085,2972,2835,2674,2489,2280,2055,1837,1631,1437,1255,1085,927,1002,1079,1158,1240,1325,1413,1504,1598,1695,1795,1898,2004,2113,2224,2333,2436,2533,2625,2711,2791,2865,2933,2995,2896,2741,2562,2359,2136,1918,1712,1518,1335,1423,1514,1608,1705,1805,1908,2014,2123,2234,2343,2446,2543,2634,2719,2798,2748,2574,2377,2157,1934,1722,1522,1618,1716,1816,1919,2025,2134,2245,2354,2457,2554,2645,2730,2809,2882,2949,3010,3065,3115,3159,3197,3229,3255,3275,3239,3168,3073,2954,2811,2644,2453,2238,2015,1803,1603,1415,1239,1075,923,782,849,919,992,1068,1147,1229,1314,1402,1493,1587,1684,1784,1887,1993,2102,2213,2323,2427,2525,2617,2703,2783,2859,2929,2993,3051,3103,3149,3189,3223,3251,3273,3292,3308,3321,3331,3338,3342,3339,3324,3297,3258,3198,3114,3006,2875,2720,2541,2338,2115,1897,1691,1497,1315,1145,987,841,707,585,475,376,422,471,523,578,636,697,761,828,898,971,1047,1126,1208,1293,1381,1472,1566,1663,1763,1866,1972,2081,2192,2303,2409,2509,2603,2691,2773,2849,2919,2983,3041,3093,3139,3179,3213,3242,3224,3152,3056,2936,2792,2624,2432,2217,1994,1782,1582,1394,1218,1054,902,762,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,877,950,1026,1105,1187,1272,1360,1451,1545,1642,1742,1845,1951,2060,2171,2282,2388,2488,2582,2670,2752,2828,2899,2860,2704,2523,2318,2094,1876,1670,1476,1294,1124,966,820,686,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,655,719,786,856,929,1005,1084,1166,1251,1339,1430,1524,1621,1721,1824,1930,2039,2150,2262,2196,1973,1761,1561,1373,1197,1033,881,741,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,873,946,1022,1101,1183,1268,1356,1447,1541,1638,1738,1841,1947,2056,2167,2278,2384,2484,2578,2666,2692,2507,2298,2073,1855,1649,1455,1273,1103,945,799,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,824,894,967,1043,1122,1204,1289,1377,1468,1562,1659,1759,1862,1968,2077,2188,2299,2405,2505,2599,2687,2769,2845,2915,2979,3037,3089,3135,3140,3039,2914,2765,2592,2395,2175,1952,1740,1540,1352,1176,1012,860,720,592,652,714,778,845,915,988,1064,1143,1225,1310,1398,1489,1583,1680,1780,1883,1989,2098,2209,2319,2423,2521,2613,2471,2256,2033,1820,1923,2029,2138,2249,2358,2461,2558,2649,2734,2813,2886,2953,3014,3069,3118,3083,2969,2832,2671,2486,2277,2052,1834,1628,1434,1252,1082,1163,1246,1331,1419,1510,1604,1701,1801,1904,2010,2119,2230,2339,2442,2539,2630,2715,2795,2869,2937,2999,3055,3105,3024,2893,2738,2559,2356,2133,1915,1709,1515,1333,1162,1244,1329,1417,1508,1602,1699,1799,1902,2008,2117,2228,2337,2440,2537,2628,2572,2374,2154,1931,1719,1821,1925,2031,2140,2251,2360,2463,2560,2651,2736,2815,2888,2955,3016,3071,3120,3163,3201,3233,3259,3279,3296,3310,3284,3236,3165,3070,2951,2808,2641,2450,2235,2012,1800,1600,1412,1236,1072,920,780,651,712,776,843,913,986,1062,1141,1223,1308,1396,1487,1581,1678,1778,1881,1987,2096,2207,2317,2421,2519,2611,2699,2781,2857,2927,2991,3049,3101,3147,3187,3221,3249,3271,3290,3306,3319,3329,3322,3295,3256,3196,3112,3004,2872,2717,2538,2335,2112,1894,1688,1494,1312,1142,984,838,704,582,472,374,287,327,370,416,465,517,572,630,691,755,822,892,965,1041,1120,1202,1287,1375,1466,1560,1657,1757,1860,1966,2075,2186,2297,2403,2503,2597,2685,2767,2843,2913,2977,3035,3087,3133,3174,3150,3054,2934,2790,2622,2430,2214,1991,1779,1579,1391,1215,1051,899,759,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,871,944,1020,1099,1181,1266,1354,1445,1539,1636,1736,1839,1945,2054,2165,2276,2382,2482,2576,2664,2747,2701,2520,2315,2091,1873,1667,1473,1291,1121,963,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,858,931,1007,1086,1168,1253,1341,1432,1526,1623,1723,1826,1932,2041,2152,2193,1970,1758,1558,1370,1194,1030,878,738,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,879,952,1028,1107,1189,1274,1362,1453,1547,1644,1744,1847,1953,2062,2173,2284,2390,2490,2584,2672,2754,2830,2850,2689,2504,2295,2070,1852,1646,1452,1270,1100,942,796,662,540,430,332,377,424,473,525,580,638,699,763,830,900,973,1049,1128,1210,1295,1383,1474,1568,1665,1765,1868,1974,2083,2194,2305,2411,2511,2605,2693,2775,2851,2921,2985,3043,3095,3141,3181,3215,3214,3137,3036,2911,2762,2589,2392,2172,1949,1737,1537,1349,1173,1009,857,717,783,851,921,994,1070,1149,1231,1316,1404,1495,1589,1686,1786,1889,1995,2104,2215,2325,2429,2527,2619,2705,2785,2659,2468,2253,2030,1818,1617,1714,1814,1917,2023,2132,2243,2352,2455,2552,2643,2728,2807,2880,2947,3008,2967,2829,2668,2483,2274,2049,1831,1625,1431,1249,1336,1425,1516,1610,1707,1807,1910,2016,2125,2236,2345,2448,2545,2636,2721,2800,2873,2941,3003,3059,3109,3153,3191,3128,3021,2890,2735,2556,2353,2130,1912,1706,1512,1330,1160,1001,1077,1156,1238,1323,1411,1502,1596,1693,1793,1896,2002,2111,2222,2331,2434,2372,2151,1928,2036,2146,2257,2366,2469,2566,2657,2742,2821,2894,2961,3022,3077,3126,3169,3206,3237,3263,3283,3300,3314,3325,3333,3315,3282,3234,3162,3067,2948,2805,2638,2447,2232,2009,1797,1597,1409,1233,1069,917,777,649,532,587,645,706,770,837,907,980,1056,1135,1217,1302,1390,1481,1575,1672,1772,1875,1981,2090,2201,2311,2415,2515,2609,2697,2779,2855,2925,2989,3047,3099,3145,3185,3219,3247,3269,3288,3304,3293,3254,3194,3110,3002,2870,2714,2535,2332,2109,1891,1685,1491,1309,1139,981,835,701,579,469,371,285,210,244,281,321,364,410,459,511,566,624,685,749,816,886,959,1035,1114,1196,1281,1369,1460,1554,1651,1751,1854,1960,2069,2180,2291,2397,2497,2591,2679,2761,2837,2907,2971,3029,3082,3052,2932,2788,2620,2428,2211,1988,1776,1576,1388,1212,1048,896,756,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,865,938,1014,1093,1175,1260,1348,1439,1533,1630,1730,1833,1939,2048,2159,2270,2376,2476,2571,2517,2312,2088,1870,1664,1470,1288,1118,960,814,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,864,937,1013,1092,1174,1259,1347,1438,1532,1629,1729,1832,1938,2047,2158,2269,2375,2410,2190,1967,1755,1555,1367,1191,1027,875,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,815,885,958,1034,1113,1195,1280,1368,1459,1553,1650,1750,1853,1959,2068,2179,2290,2396,2496,2590,2678,2760,2836,2906,2970,2984,2847,2686,2501,2292,2067,1849,1643,1449,1267,1097,939,793,659,537,427,478,531,586,644,705,769,836,906,979,1055,1134,1216,1301,1389,1480,1574,1671,1771,1874,1980,2089,2200,2310,2147,2258,2367,2470,2567,2658,2743,2822,2895,2962,3023,3078,3127,3170,3207,3238,3212,3134,3033,2908,2759,2586,2389,2169,1946,1734,1534,1346,1170,1006,854,926,1000,1076,1155,1237,1322,1410,1501,1595,1692,1792,1895,2001,2110,2221,2330,2433,2531,2623,2709,2789,2863,2931,2823,2656,2465,2250,2027,1815,1615,1426,1517,1611,1708,1808,1911,2017,2126,2237,2346,2449,2546,2637,2722,2801,2874,2827,2665,2480,2271,2046,1828,1622,1428,1521,1616,1713,1813,1916,2022,2131,2242,2351,2454,2551,2642,2727,2806,2879,2946,3007,3063,3113,3157,3195,3227,3253,3208,3125,3018,2887,2732,2553,2350,2127,1909,1703,1509,1327,1157,999,852,922,995,1071,1150,1232,1317,1405,1496,1590,1687,1787,1890,1996,2105,2216,2149,2261,2370,2473,2570,2661,2746,2825,2898,2965,3026,3081,3130,3173,3210,3241,3266,3286,3303,3317,3328,3336,3341,3343,3334,3313,3280,3232,3160,3064,2945,2802,2635,2444,2229,2006,1794,1594,1406,1230,1066,914,774,646,530,425,474,526,581,639,700,764,831,901,974,1050,1129,1211,1296,1384,1475,1569,1666,1766,1869,1975,2084,2195,2306,2412,2512,2606,2694,2776,2852,2922,2986,3044,3096,3142,3182,3216,3244,3267,3252,3192,3108,3000,2868,2712,2532,2329,2106,1888,1682,1488,1306,1136,978,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,880,953,1029,1108,1190,1275,1363,1454,1548,1645,1745,1848,1954,2063,2174,2285,2391,2491,2585,2673,2755,2831,2901,2966,2930,2786,2618,2425,2208,1985,1773,1573,1385,1209,1045,893,753,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,859,932,1008,1087,1169,1254,1342,1433,1527,1624,1724,1827,1933,2042,2153,2264,2371,2309,2085,1867,1661,1467,1285,1115,957,811,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,870,943,1019,1098,1180,1265,1353,1444,1538,1635,1735,1838,1944,2053,2164,2275,2381,2481,2575,2604,2407,2187,1964,1752,1552,1364,1188,1024,872,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,821,891,964,1040,1119,1201,1286,1374,1465,1559,1656,1756,1859,1965,2074,2185,2296,2402,2502,2596,2684,2766,2842,2912,2976,3034,3086,3094,2981,2844,2683,2498,2289,2064,1846,1640,1446,1264,1094,936,790,656,534,591,650,711,775,842,912,985,1061,1140,1222,1307,1395,1486,1580,1677,1777,1880,1986,2095,2206,2316,2420,2518,2368,2145,1926,2032,2141,2252,2361,2464,2561,2652,2737,2816,2889,2956,3017,3072,3121,3164,3132,3030,2905,2756,2583,2386,2166,1943,1731,1531,1343,1167,1003,1081,1161,1243,1328,1416,1507,1601,1698,1798,1901,2007,2116,2227,2336,2439,2536,2627,2713,2793,2867,2935,2997,3053,2963,2820,2653,2462,2247,2024,1812,1612,1424,1247,1332,1420,1511,1605,1702,1802,1905,2011,2120,2231,2340,2443,2540,2631,2716,2663,2477,2268,2043,1825,1619,1718,1819,1922,2028,2137,2248,2357,2460,2557,2648,2733,2812,2885,2952,3013,3068,3117,3161,3199,3231,3257,3277,3294,3264,3205,3122,3015,2884,2729,2550,2347,2124,1906,1700,1506,1324,1154,996,850,715,779,846,916,989,1065,1144,1226,1311,1399,1490,1584,1681,1781,1884,1990,2099,2210,2320,2424,2522,2614,2700,2782,2858,2928,2992,3050,3102,3148,3188,3222,3250,3272,3291,3307,3320,3330,3337,3332,3311,3278,3230,3158,3062,2942,2799,2632,2441,2226,2003,1791,1591,1403,1227,1063,911,771,643,527,423,330,373,419,468,520,575,633,694,758,825,895,968,1044,1123,1205,1290,1378,1469,1563,1660,1760,1863,1969,2078,2189,2300,2406,2506,2600,2688,2770,2846,2916,2980,3038,3090,3136,3176,3211,3190,3106,2998,2866,2710,2530,2326,2103,1885,1679,1485,1303,1133,975,829,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,874,947,1023,1102,1184,1269,1357,1448,1542,1639,1739,1842,1948,2057,2168,2279,2385,2485,2579,2667,2749,2826,2784,2615,2422,2205,1982,1770,1570,1382,1206,1042,890,750,622,506,402,310,230,162,106,62,30,10)

Conjugacy classes & character table

2234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20058, 2);

C2×C3343⋊C3 #34095385