Finite Group DatabasebetaFinite Group Databasebeta| order | 20105 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C4021⋊C5 |
| Fitting, socle, derived, Sylow | C4021 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C4021 | C5 |
| LCS | G ▷ C4021 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 4021 |
| transitive degree | μt(G) = 4021 |
A minimal faithful permutation representation — 2 generators on 4021 points:
(2,3,5,9,17)(4,7,13,25,48)(6,11,21,40,33)(8,15,29,56,105)(10,19,36,18,34)(12,23,44,82,90)(14,27,52,97,64)(16,31,60,113,204)(20,38,71,49,91)(22,42,78,75,65)(24,46,86,155,189)(26,50,93,35,66)(28,54,101,181,163)(30,58,109,196,121)(32,62,117,212,366)(37,69,41,76,68)(39,73,133,106,190)(43,80,144,148,164)(45,84,151,174,122)(47,88,159,275,351)(51,95,170,92,165)(53,99,177,137,123)(55,103,185,317,325)(57,107,192,67,124)(59,111,200,343,283)(61,115,208,358,220)(63,119,216,373,611)(70,128,83,149,167)(72,131,98,175,126)(74,135,238,205,352)(77,139,130,94,168)(79,142,141,138,127)(81,146,253,268,326)(85,153,264,310,284)(87,157,271,336,221)(89,161,279,461,600)(96,172,295,191,327)(100,179,306,257,285)(102,183,313,299,222)(104,187,321,524,574)(108,194,332,166,286)(110,198,339,242,223)(112,202,347,566,532)(114,206,354,125,224)(116,210,362,592,469)(118,214,369,604,381)(120,218,377,619,963)(129,229,156,269,329)(132,233,182,311,288)(134,236,197,337,226)(136,240,211,364,596)(140,245,235,193,330)(143,248,250,258,289)(145,251,261,300,227)(147,255,424,454,575)(150,259,292,169,290)(152,262,303,243,228)(154,266,439,517,533)(158,273,450,559,470)(160,277,457,585,382)(162,281,465,733,949)(171,293,176,301,231)(173,297,487,353,576)(178,304,247,244,232)(180,308,502,443,534)(184,315,513,506,471)(186,319,520,548,383)(188,323,528,821,932)(195,334,544,328,535)(199,341,555,428,472)(201,345,562,491,384)(203,349,570,883,891)(207,356,581,287,473)(209,360,588,409,385)(213,367,601,225,386)(215,371,608,944,741)(217,375,615,956,627)(219,379,623,970,1431)(230,392,276,455,578)(234,397,318,518,537)(237,401,344,560,475)(239,404,359,586,388)(241,407,460,612,950)(246,413,403,355,579)(249,416,421,444,538)(252,419,436,507,476)(254,422,447,549,389)(256,426,656,727,925)(260,431,484,331,539)(263,434,499,429,477)(265,437,510,492,390)(267,441,698,814,892)(270,445,541,291,478)(272,448,552,410,391)(274,452,713,876,829)(278,459,724,918,742)(280,463,622,937,628)(282,467,737,1109,1420)(294,482,312,508,480)(296,485,338,550,394)(298,489,766,597,926)(302,494,399,333,542)(305,497,418,430,481)(307,500,433,493,395)(309,504,785,717,893)(314,511,496,411,396)(316,515,799,803,830)(320,522,810,865,743)(322,526,817,907,629)(324,530,825,1223,1397)(335,546,846,577,894)(340,553,415,412,400)(342,557,861,702,831)(346,564,872,788,744)(348,568,879,850,630)(350,572,887,1306,1372)(357,583,903,536,832)(361,590,914,683,745)(363,594,921,770,631)(365,598,928,414,666)(368,602,934,474,746)(370,606,940,661,632)(372,605,938,635,406)(374,613,952,387,633)(376,617,960,1415,1116)(378,621,967,1426,978)(380,625,974,1437,2005)(393,640,462,728,933)(398,646,525,815,896)(402,651,567,877,834)(405,655,593,919,748)(408,659,820,964,1421)(417,669,677,718,897)(420,672,695,804,835)(423,675,710,866,749)(425,678,721,908,636)(427,681,1035,1102,1398)(432,687,763,580,898)(435,690,782,703,836)(438,693,796,789,750)(440,696,807,851,637)(442,700,1059,1216,1361)(446,705,843,540,837)(449,708,858,684,751)(451,711,869,771,638)(453,715,1078,1299,1314)(456,719,900,479,752)(458,722,911,662,639)(464,731,1099,1389,1117)(466,735,1105,1408,979)(468,739,1112,1594,1995)(483,757,519,805,839)(486,761,561,867,754)(488,764,587,909,642)(490,768,1148,951,1399)(495,774,653,582,901)(498,777,674,704,840)(501,780,692,790,755)(503,783,707,852,643)(505,787,1171,1094,1362)(509,791,759,543,841)(512,794,779,685,756)(514,797,793,772,644)(516,801,1188,1206,1315)(521,808,855,663,645)(523,812,1202,1288,1230)(527,819,1213,1350,1118)(529,823,1219,1378,980)(531,827,1226,1730,1979)(545,844,551,853,648)(547,848,1252,927,1363)(554,856,671,686,760)(556,859,689,773,649)(558,863,1270,1082,1316)(563,870,776,664,650)(565,874,1284,1191,1231)(569,881,1295,1273,1119)(571,885,1302,1335,981)(573,889,1310,1832,1945)(584,905,1331,895,1317)(589,912,668,665,654)(591,916,1346,1063,1232)(595,923,1357,1173,1120)(599,930,1368,775,1157)(603,935,1375,833,1233)(607,942,1385,1040,1121)(609,946,1392,1152,982)(610,941,1383,1024,1021)(614,954,1404,747,1122)(616,958,1411,1016,983)(618,945,1390,1124,657)(620,965,1423,634,984)(624,972,1435,2001,1445)(626,976,1441,2011,2636)(641,992,734,1103,1401)(647,999,822,1217,1373)(652,1005,884,1300,1319)(658,732,957,1409,986)(660,1014,1305,1432,1996)(667,1022,726,953,1402)(670,1025,1010,1095,1365)(673,1028,1056,1207,1320)(676,1031,1075,1289,1235)(679,1034,1090,1351,1125)(680,1011,969,1379,987)(682,1038,1505,1589,1980)(688,1045,1145,929,1366)(691,1048,1168,1083,1321)(694,1051,1185,1192,1236)(697,1054,1199,1274,1126)(699,1057,1210,1336,988)(701,1061,1530,1725,1946)(706,1067,1249,899,1322)(709,1070,1267,1064,1237)(712,1073,1281,1174,1127)(714,1076,1292,1256,989)(716,1080,1553,1825,1896)(720,1085,1328,838,1238)(723,1088,1343,1041,1128)(725,1091,1354,1153,990)(729,1096,1374,753,1129)(730,973,1382,1017,991)(736,1107,1586,1971,1601)(738,1111,1592,1988,1446)(740,1114,1597,2171,2627)(758,1135,816,1208,1324)(762,1140,878,1290,1240)(765,1144,920,1352,1131)(767,1146,939,1380,994)(769,1150,1638,1422,1981)(778,1160,1033,1084,1325)(781,1163,1053,1193,1241)(784,1166,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6,3301,3731,3028,3521,3848,3862,3945,1114,1598,2149,360,589,913,1342,1871,2463,3046,2359,482,756,1133,1618,2192,2799,1390,1934,2534,3111,2864,3405,3793,3834,1681,253,421,674,1030,1498,2068,2692,3273,3712,3946,2135,334,545,845,1248,1755,2337,2935,2331,2929,3455,3526,3298,3729,3618,1394,1941,2543,3121,3584,3873,3009,3504,1657,233,396,644,996,1463,2033,919,1351,1882,2474,2109,2728,3302,3415,1057,86,156,270,446,706,1068,1540,2110,2730,3305,1348,1879,2471,2561,3137,3595,3879,3830,1621,2195,2801,2943,3465,3827,3114,3578,3870,3902,3982,2644,3234,2311,2908,1031,54,102,184,316,516,802,560,866,1274,1784,1254,1763,2345,2738,526,818,1212,1710,2288,2887,1822,2405,2988,3490,3127,3591,3878,3890,1908,2504,3082,3553,3387,999,1466,2035,2215,2823,3376,2477,3056,3536,3590,3733,3956,3817,1590,2161,452,714,1077,1549,2118,2735,1806,311,507,789,1174,1665,2239,2842,1830,2417,3000,3499,3359,3763,3206,1213,1711,2289,2888,3422,3804,3984,3573,1329,1855,2446,3030,2693,323,529,824,1222,1724,2303,1787,2368,2957,3069,2946,3468,3339,965,1424,1985,2598,3178,3633,3905,3491,1197,149,258,429,684,1041,1510,2081,2704,3283,3718,3950,2663,3249,2604,724,1090,1566,2137,2751,3320,3742,3051,844,1246,1752,2333,1555,2125,1974,2584,621,968,1429,1177,1668,2242,2382,2968,3478,2626,3212,3665,3230,3679,2318,2918,3448,2889,708,50,94,169,291,479,753,1130,1615,2189,2798,3356,1228,1734,1962,362,593,920,1353,1885,2478,3058,2362,485,760,1138,1624,2199,2806,1392,1937,2538,3116,2867,687,1044,1513,1683,2256,2856,3400,3791,3981,2636,3223,3674,3927,3907,2138,341,556,860,1266,1775,2357,2951,2336,2933,3458,3527,3314,3737,3620,1380,1920,2517,3095,2847,3393,3011,3506,1660,236,400,649,1002,1470,2040,921,1354,1886,2479,2112,297,488,765,1059,1527,2095,2716,3292,3726,2005,2627,2922,3453,3605,1359,1893,2487,2563,3139,3596,3003,3500,1627,2202,2809,2944,3466,3828,3117,909,1337,1865,2457,2086,2708,2313,2910,1034,58,110,199,342,558,864,562,869,1278,1789,1272,1783,2365,2740,528,822,1218,1718,2296,2896,1431,1995,2612,3193,3098,3567,3865,3891,1915,2512,3091,2305,2903,1005,1473,2043,2216,2824,3377,2480,550,852,1257,1766,1150,1639,1592,2163,459,725,1092,1568,2139,2753,1809,313,510,793,1179,1671,2246,2849,1834,2423,3007,3503,3365,3767,3209,963,1420,1979,2592,2460,3043,3529,3574,1331,1857,2448,1581,2152,349,571,886,1305,1824,2408,1790,301,493,772,1154,1644,2220,967,1427,1990,2605,3185,3639,3908,3195,1200,151,261,433,689,1047,1517,2088,2711,3288,3722,3952,2670,3254,2607,611,949,1397,1945,1769,2352,2947,3052,846,1249,1756,954,1405,1955,2559,3135,623,971,1434,1180,139,244,411,663,1018,1486,2056,2681,3262,3703,3941,3846,3995,2594,711,52,98,176,302,495,775,1158,1649,2225,2831,3381,1312,1836,1965,366,600,932,1372,1157,1647,2222,2364,487,763,1142,1629,2205,2813,3367,2173,2785,3343,2869,690,38,72,132,234,398,647,1000,1468,2038,2664,3251,3450,3819,1947,345,563,871,1280,1791,2372,1306,1825,2409,2991,2565,3143,3600,3622,1383,204,351,574,891,666,1021,1488,1662,238,403,653,1007,1476,2047,2672,3256,3699,3904,2114,308,503,784,1167,1658,2234,2839,3388,3784,3977,4016,3017,2786,3344,1363,1898,2492,3071,2830,3379,3006,821,1216,1715,2292,2891,3425,3805,3120,912,105,189,325,532,240,406,657,1011,60,114,207,357,584,906,1334,1863,2456,3040,1286,1799,2381,2741,3310,3735,2994,3494,3836,3672,3886,4003,3964,2011,2637,894,1316,1840,2431,2060,2683,2308,461,727,1094,1570,2141,2755,3322,2483,553,48,90,163,283,469,741,1116,463,730,1098,1575,2147,2761,1811,2392,2975,3481,3074,3548,3857,3881,1835,2425,3010,2295,2894,3428,3211,3663,3920,3684,3933,2462,535,831,1231,1737,1014,1481,1584,212,364,597,927,1364,1900,2495,1793,304,17,33,64,121,220,381,627,978,1445,2017,2646,3235,3199,1202,1697,2272,2871,2434,3020,3516,3557,3705,3942,3814,1573,2144,2758,2609,3189,3643,3910,3855,1771,286,472,744,1119,1603,2178,958,1412,1966,2573,3151,3607,3887,3482,1183,142)Polycyclic presentation:
5,4021|b^a=b^2708809 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20105, 1);