Finite Group Databasebeta

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C₄₂₆₁⋊C₅ #36319193

• 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 4261 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)(32,62,117,212,365)(37,69,41,76,68)(39,73,133,106,190)(43,80,144,148,164)(45,84,151,174,122)(47,88,159,275,350)(51,95,170,92,165)(53,99,177,137,123)(55,103,185,316,324)(57,107,192,67,124)(59,111,200,342,282)(61,115,208,357,220)(63,119,216,280,463)(70,128,83,149,167)(72,131,98,175,126)(74,135,238,205,351)(77,139,130,94,168)(79,142,141,138,127)(81,146,253,268,325)(85,153,264,309,283)(87,157,271,335,221)(89,161,279,461,597)(96,172,294,191,326)(100,179,305,257,284)(102,183,312,298,222)(104,187,320,522,571)(108,194,331,166,285)(110,198,338,242,223)(112,202,346,563,529)(114,206,353,125,224)(116,210,361,589,467)(118,214,369,604,380)(120,218,376,615,951)(129,229,156,269,328)(132,233,182,310,287)(134,236,197,336,226)(136,240,405,366,598)(140,245,235,193,329)(143,248,250,258,288)(145,251,261,299,227)(147,255,424,454,572)(150,259,291,169,289)(152,262,302,243,228)(154,266,439,515,530)(158,273,450,556,468)(160,277,457,582,381)(162,281,465,730,727)(171,292,176,300,231)(173,296,485,352,573)(178,303,247,244,232)(180,307,500,443,531)(184,314,511,504,469)(186,318,518,545,382)(188,322,526,814,923)(195,333,541,327,532)(199,340,552,428,470)(201,344,559,489,383)(203,348,567,874,881)(207,355,578,286,471)(209,359,585,409,384)(211,363,593,915,819)(213,367,600,225,385)(215,371,608,940,734)(217,374,527,815,623)(219,378,619,958,1393)(230,391,276,455,575)(234,396,317,516,534)(237,400,343,557,473)(239,403,358,583,387)(241,407,654,464,728)(246,413,402,354,576)(249,416,421,444,535)(252,419,436,505,474)(254,422,447,546,388)(256,426,677,724,924)(260,431,482,330,536)(263,434,497,429,475)(265,437,508,490,389)(267,441,694,807,882)(270,445,538,290,476)(272,448,549,410,390)(274,452,709,867,820)(278,459,720,908,735)(293,480,311,506,478)(295,483,337,547,393)(297,487,758,599,925)(301,492,398,332,539)(304,495,418,430,479)(306,498,433,491,394)(308,502,777,713,883)(313,509,494,411,395)(315,513,792,796,821)(319,520,803,856,736)(321,524,810,897,624)(323,528,817,1192,1083)(334,543,837,574,884)(339,550,415,412,399)(341,554,852,698,822)(345,561,863,781,737)(347,565,870,841,625)(349,569,878,1275,1342)(356,580,893,533,823)(360,587,904,679,738)(362,591,911,762,626)(364,595,919,1335,1280)(368,602,930,472,739)(370,606,936,658,627)(372,610,944,1371,1195)(373,466,732,386,628)(375,613,879,1276,1092)(377,617,954,1386,966)(379,621,962,1400,1915)(392,635,462,725,927)(397,641,523,808,886)(401,645,564,868,825)(404,649,590,909,740)(406,652,605,934,630)(408,656,1000,952,1382)(414,663,651,601,928)(417,666,674,714,887)(420,669,691,797,826)(423,672,706,857,741)(425,675,717,898,631)(427,678,1023,1087,1084)(432,683,755,577,888)(435,686,774,699,827)(438,689,789,782,742)(440,692,800,842,632)(442,696,1043,1189,1343)(446,701,834,537,828)(449,704,849,680,743)(451,707,860,763,633)(453,711,1060,1268,1281)(456,715,890,477,744)(458,718,901,659,634)(460,722,1075,1328,1196)(481,749,517,798,830)(484,753,558,858,746)(486,756,584,899,637)(488,760,1120,729,1085)(493,766,647,579,891)(496,769,671,700,831)(499,772,688,783,747)(501,775,703,843,638)(503,779,1142,1079,1344)(507,784,751,540,832)(510,787,771,681,748)(512,790,786,764,639)(514,794,1159,1178,1282)(519,801,846,660,640)(521,805,1174,1257,1197)(525,812,1185,1317,1093)(542,835,548,844,642)(544,839,1219,926,1345)(551,847,668,682,752)(553,850,685,765,643)(555,854,1238,1064,1283)(560,861,768,661,644)(562,865,1253,1163,1198)(566,872,1264,1242,1094)(568,876,1271,1302,967)(570,880,1278,1748,1527)(581,895,1298,885,1284)(586,902,665,662,648)(588,906,1313,1045,1199)(592,913,1324,1144,1095)(594,917,1331,1223,968)(596,921,1339,1831,1836)(603,932,1353,824,1200)(607,938,1361,1024,1096)(609,942,1367,1124,969)(611,946,1375,1879,1751)(612,818,1193,1004,970)(614,949,1340,1832,1648)(616,953,1384,629,971)(618,956,1389,1897,1537)(620,960,1396,1908,1408)(622,964,1404,1922,2474)(636,977,731,1088,1089)(646,987,875,1269,1286)(650,991,916,1329,1201)(653,995,941,1365,1097)(655,998,816,1190,973)(657,1002,1443,1394,1904)(664,1009,997,733,1090)(667,1012,1022,1080,1347)(670,1015,1040,1179,1287)(673,1017,1057,1258,1202)(676,1020,1072,1318,1098)(684,1029,1117,929,1348)(687,1032,1139,1065,1288)(690,1035,1156,1164,1203)(693,1038,1171,1243,1099)(695,1041,1182,1303,974)(697,1044,1481,1645,1528)(702,1049,1216,889,1289)(705,1052,1235,1046,1204)(708,1055,1250,1145,1100)(710,1058,1261,1224,975)(712,1062,1501,1745,1837)(716,1067,1295,829,1205)(719,1070,1310,1025,1101)(721,1073,1321,1125,976)(723,1077,1518,1824,1752)(726,1081,1350,745,1102)(750,1107,809,1180,1291)(754,1111,869,1259,1207)(757,1115,910,1319,1103)(759,1118,935,1357,978)(761,1122,1567,1383,1889)(767,1129,993,931,1351)(770,1131,1019,1066,1292)(773,1134,1037,1165,1208)(776,1137,1054,1244,1104)(778,1140,1069,1304,979)(780,1143,1587,1532,1529)(785,1148,1113,892,1293)(788,1151,1136,1047,1209)(791,11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Polycyclic presentation:

5,4261|b^a=b^398

Conjugacy classes & character table

857 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21305, 1);