Finite Group Databasebeta

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C₃₆₉₇⋊C₇ #39905583

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3697 points:

(2,3,5,9,17,33,65)(4,7,13,25,49,97,191)(6,11,21,41,81,124,129)(8,15,29,57,113,223,431)(10,19,37,73,144,66,130)(12,23,45,89,175,338,369)(14,27,53,105,207,399,254)(16,31,61,121,239,463,861)(18,35,69,136,34,67,132)(20,39,77,152,293,192,370)(22,43,85,167,322,245,255)(24,47,93,183,354,662,800)(26,51,101,199,384,131,256)(28,55,109,215,415,771,689)(30,59,117,231,447,829,490)(32,63,125,246,475,880,661)(36,71,140,272,98,193,372)(38,75,148,286,160,249,258)(40,79,156,301,564,432,801)(42,83,163,314,280,133,259)(44,87,171,330,615,631,690)(46,91,179,346,646,741,491)(48,95,187,362,677,1195,1498)(50,99,195,376,68,134,261)(52,103,203,392,729,371,691)(54,107,211,407,756,474,492)(56,111,219,423,576,143,278)(58,115,227,439,814,257,493)(60,119,235,455,845,1467,1216)(62,123,243,470,872,1511,907)(64,127,250,482,892,788,1372)(70,138,268,82,161,310,265)(72,142,276,524,224,433,803)(74,146,151,145,281,137,266)(76,150,290,545,339,632,693)(78,154,297,557,400,742,495)(80,158,305,572,1024,862,1499)(84,165,318,593,550,373,694)(86,169,326,608,601,481,496)(88,173,334,623,895,1170,1393)(90,177,342,638,715,260,497)(92,181,350,654,1155,1346,1217)(94,185,358,669,1180,1439,908)(96,189,365,683,1205,1953,1169)(100,197,380,707,194,374,696)(102,201,388,722,309,485,499)(104,205,396,706,1241,802,664)(106,209,403,748,531,262,500)(108,213,411,764,1336,1119,1218)(110,217,419,234,453,841,909)(112,221,427,793,1381,969,1639)(114,225,435,807,135,263,502)(116,229,443,822,1426,692,1219)(118,233,451,837,1453,879,910)(120,237,459,853,1483,1590,528)(122,241,466,866,1503,494,911)(126,248,479,887,1532,2382,1563)(128,252,486,899,1548,1646,1055)(139,270,513,176,340,634,700)(141,274,520,208,401,744,506)(147,284,329,294,551,377,701)(149,288,391,323,602,580,507)(153,295,553,385,716,267,508)(155,299,561,1006,772,1347,1221)(157,303,568,1017,830,1440,913)(159,307,575,1030,1478,1523,1194)(162,312,583,517,196,378,703)(164,316,590,539,311,581,510)(166,320,597,1062,1011,804,1395)(168,324,604,587,532,269,511)(170,328,612,1086,1091,1120,1222)(172,332,619,1098,1143,1298,914)(174,336,627,1112,1830,1942,2349)(178,344,642,1136,1279,695,1223)(180,348,650,1148,1322,891,915)(182,352,658,1163,1369,279,529)(184,356,665,1173,1413,498,916)(186,360,673,1187,1929,2300,1971)(188,364,681,1201,1947,2360,1564)(190,367,686,1211,1963,2818,2173)(198,382,711,1250,434,805,1397)(200,386,718,282,533,273,518)(202,390,726,1274,633,1121,1225)(204,394,733,1286,743,1299,918)(206,302,566,1014,815,1414,509)(210,405,752,1314,989,697,1226)(212,409,760,1329,1069,898,919)(214,413,768,1342,2138,1911,1172)(216,417,775,1353,1257,501,920)(218,421,782,672,1185,1926,1972)(220,425,789,1020,586,1045,1565)(222,429,796,1387,2193,2025,1910)(226,437,811,1407,375,698,1228)(228,441,818,1420,579,902,922)(230,445,826,1434,2254,1394,1175)(232,449,833,1446,965,503,923)(236,457,849,1475,2313,1461,1566)(238,461,857,1491,2338,2591,2492)(240,464,863,560,264,504,925)(242,468,868,1506,2354,1220,1973)(244,472,875,1516,2365,1522,1567)(247,477,883,1526,2375,912,1568)(251,484,896,1543,1902,2761,2415)(253,488,903,1555,2402,2633,2622)(271,515,940,355,663,1171,1401)(275,522,951,416,773,1349,1232)(277,526,958,448,831,1442,929)(283,300,287,540,315,588,292)(285,537,653,565,1012,808,1402)(289,543,763,616,1092,1123,1233)(291,547,821,647,1144,1301,930)(296,555,996,730,1280,702,1234)(298,559,1003,757,1323,1036,931)(304,570,1021,1705,1468,2209,1975)(306,574,1028,1715,1512,2361,1570)(308,577,1032,1722,2570,1373,2174)(313,585,1043,955,436,809,1404)(317,592,1054,982,635,1124,1236)(319,595,1059,1000,745,1302,933)(321,599,523,953,1619,786,1033)(325,606,1076,1056,990,704,1237)(327,610,1083,1080,1070,1037,934)(331,617,1094,1130,1258,512,935)(333,621,1102,1815,1888,2144,1976)(335,625,1108,1823,1921,2262,1571)(337,629,1115,1836,2694,2808,1941)(341,636,1126,1243,379,705,1239)(343,640,1133,1267,582,1038,937)(345,644,1140,1867,2000,1396,1182)(347,648,1146,1308,966,514,938)(349,652,1152,1883,2131,1840,1977)(351,656,1159,1893,842,1462,1572)(353,660,1167,1907,2768,1640,2493)(357,667,1176,1915,2241,1224,1978)(359,671,1183,1923,2281,1538,1573)(361,675,1191,1936,2796,2441,962)(363,679,395,735,1290,917,1348)(366,685,1209,1959,2813,3198,2416)(368,688,1214,1968,2825,2887,1750)(381,709,1246,402,746,1304,944)(383,713,921,1578,424,787,1116)(387,720,1263,552,991,708,1244)(389,724,1270,603,1071,1040,945)(393,731,1282,717,578,519,946)(397,738,1273,2043,1441,1820,1575)(398,569,1019,1703,1454,2282,1726)(404,750,1311,974,584,1041,948)(406,754,1318,2103,1691,1398,2205)(408,758,1325,1047,967,521,949)(410,762,1333,2126,1799,1841,1980)(412,766,1338,2133,1872,2078,1576)(414,573,1026,1712,1504,2352,932)(418,777,1357,2158,2053,1227,1981)(420,780,473,877,1518,1547,1577)(422,784,1367,1376,2177,530,963)(426,791,1377,1826,1307,2088,2830)(428,795,1385,2074,1772,2618,2417)(430,798,1390,2199,1967,2824,3020)(438,813,1411,2219,806,1399,1529)(440,816,1416,534,968,525,956)(442,820,1424,2237,1122,1842,1982)(444,824,1430,2248,1300,2079,1580)(446,624,1106,1551,1913,2223,936)(450,835,1450,2276,1662,122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911,1008,1688,2534,1280,2054,2909,3012,663,508,931,1591,1261,2027,2877,3487,640,1134,1858,2257,1226,1980,1199,1944,595,1060,1757,2606,3332,3658,877,1519,526,959,1475,2314,3148,3614,2155,2825,2563,3261,1457,2289,3120,777,1358,2161,2550,3297,1424,2238,3067,652,1153,1886,927,1587,632,1120,1840,421,783,1366,2167,3017,3433,2956,437,812,1410,2139,2455,3240,3428,3490,390,727,1277,2051,2906,3195,3418,3469,299,562,1009,1689,2535,2768,2121,2972,119,236,458,852,1482,2323,2093,2395,3154,3114,1331,2124,2976,2750,3422,2391,2569,3098,1276,2049,57,114,226,438,127,251,485,898,1547,2394,3204,2358,2201,3045,3383,2865,2356,3183,3579,1822,2677,3380,3377,41,82,162,313,586,1046,1740,2590,21,42,84,166,321,600,1068,1767,1513,2362,3073,1147,901,1553,2401,1995,1501,2350,3058,1085,1791,2639,2658,3365,3634,1530,2380,986,1658,2507,2627,3347,3453,3007,3557,493,910,1566,2418,3221,3450,3682,3462,3301,3611,2250,3083,3586,1178,1919,2780,3291,2361,3186,3341,3660,843,1465,2299,3130,1469,2303,3132,3197,2147,2997,2558,3252,1448,2274,3103,754,1319,2106,2541,3217,1409,2217,152,294,552,992,1666,2513,3279,3650,2384,352,659,1166,1906,2767,3430,2951,2377,3194,3601,191,369,689,1216,81,160,309,579,1035,1725,2574,2405,69,137,267,509,932,1592,2442,2111,2962,958,1627,1351,2149,2998,2199,2082,2936,3129,3605,1313,2096,2949,1966,2823,557,1000,1676,1248,2010,51,102,202,391,728,1278,2052,2907,1491,2339,3169,513,937,1597,2446,2855,1385,2190,3031,1808,2661,3368,3373,35,70,139,271,516,943,1607,2459,11,22,44,88,174,337,630,1118,849,1476,2316,1128,1849,2707,3089,1978,782,1364,199,385,717,1259,2025,475,658,1164,1902,953,1620,2472,3253,466,427,794,1384,2189,3030,2286,3115,443,823,1429,2247,3078,3583,2236,1407,396,737,1293,1086,1792,2640,3354,3665,305,573,1027,1059,1755,2604,3330,3657,125,247,478,886,1531,2381,814,1413,713,1254,615,1091,1799,2649,803,146,283,535,604,1073,1773,2620,3343,1936,221,428,583,1040,1731,2580,2944,1903,2762,3431,2118,2869,3481,2827,3464,1827,2683,3384,2043,2894,3495,2400,1201,983,1654,2504,2067,2925,3518,3398,1183,949,1613,2464,2041,2891,2195,3036,1152,1884,223,432,802,1394,1961,2815,551,990,1663,1867,2725,39,78,155,300,563,1010,1690,2536,1485,2327,3157,500,919,1576,2426,2841,1375,1446,2270,1781,2629,1148,1878,2736,1189,1933,2570,1651,2500,1133,1856,873,855,1488,2333,3162,2348,3181,3317,839,1458,2291,2561,3256,3642,3077,3582,766,1339,193,373,695,1224,1979,2834,625,1109,1826,1761,2609,2413,2982,3209,364,682,1204,1952,2807,2268,2954,3207,3396,2354,2135,2438,3232,2138,1402,2210,1067,1381,1081,1784,2633,2132,2986,3202,629,1116,1052,1746,2595,2116,2967,2770,3180,1357,2159,3008,3558,2087,2941,2692,3390,1318,2104,2957,1915,2776,134,262,501,921,1579,2429,3228,3591,1930,1625,2478,3258,2902,3503,3689,2935,1895,1467,2300,2088,2859,1180,1921,2782,1817,2673,3378,2001,2850,1171,1912,1196,976,1647,2497,2058,2913,3509,3561,1174,935,1595,2444,2029,2878,2188,3028,1138,1865,2722,3092,1983,2836,1951,2806,1064,1764,2330,1862,2717,15,30,60,120,238,462,860,1497,1473,2311,3144,3307,3645,2292,3125,2831,1362,1440,2262,1739,2588,1144,1873,2732,1161,1898,2758,1606,2457,1124,1843,864,791,1378,2181,3025,3565,3679,3532,820,1425,2240,2993,3242,3632,3060,3578,735,1291,2072,2931,3522,246,476,882,570,1022,1708,1753,2602,3328,2975,65,129,254,490,907,1563,2415,2948,3205,3393,3597,2128,2983,183,355,664,1172,963,1633,1071,1770,117,232,450,836,367,687,1038,1728,2577,3312,3655,2761,3048,3575,3671,105,208,402,747,1307,2089,2943,2884,85,168,325,607,1079,1782,2631,2923,45,90,178,345,645,1142,1871,2731,2363,3187,3581,1882,1557,2406,3211,2848,2351,2811,3457,1797,2647,3358,3367,3668,3684,2388,3203,968,1638,2491,3268,3649,3683,3559,3686,916,1573,2424,3224,3637,2174,3021,1953,2808,3189,3085,3588,572,1025,1711,2559,2495,2324,1854,2711,3400,1481,2322,3155,3618,2308,3140,3610,1452,2280,3109,707,1243,2003,2853,330,616,1093,1802,2653,3360,2221,3056,297,558,1002,1679,2525,3286,3651,3547,3201,675,1192,384,715,1257,2023,175,339,633,1122,372,693,1221,1975,163,315,589,1050,1744,2593,241,467,140,273,519,947,1611,2462,3178,2966,3536,1629,2481,2157,3005,3556,3044,2940,1017,1700,2545,2102,2955,177,343,641,1003,1680,2526,2018,2870,107,212,410,763,1335,2130,2985,3501,2342,3173,3626,940,1601,2450,3237,99,196,379,706,1242,2002,2852,2840,75,149,289,544,981,1652,2502,2910,27,54,108,214,414,770,748,1308,1479,2318,407,757,1324,2112,2964,892,1367,2168,388,723,1269,2037,2888,883,1167,1908,2771,1631,2484,3151,3617,868,796,1388,2196,3038,3570,3123,2237,826,1435,2256,1815,2669,3374,3070,2216,566,1015,1697,1795,2440,3234,1842,2701,575,1031,1721,1758,2607,3333,1426,2241,250,483,895,701,1233,1990,1416,324,605,1075,1094,1803,2654,3361,1397,288,542,978,1076,1776,2623,3345,3541,2799,461,858,1043,1735,2584,3316,3526,2765,3434,822,1427,2243,3072,3467,1959,1685,2531,3289,2905,3506,229,444,825,1433,488,904,1558,2407,771,1346,1926,1617,447,830,1441,2263,3041,3107,1012,1692,435,808,1403,165,319,596,994,1668,2515,2728,3410,87,172,333,622,1104,1819,2674,3379,2332,2288,3118,923,1581,1893,2751,3423,2180,2273,731,1283,2059,1881,2740,1533,1938,2800,3310,2509,3277,1859,2715,1517,1493,2343,3175,1568,2419,742,1298,1462,2294,401,745,1303,2083,2938,3053,1344,2141,378,704,1238,1996,2846,3471,1114,1835,2693,2612,3336,3135,3550,3635,685,1210,1962,2817,866,1504,2232,3062,2108,2193,1811,2664,3370,2991,2211,555,997,1672,1788)

Polycyclic presentation:

7,3697|b^a=b^2297

Conjugacy classes & character table

535 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25879, 1);