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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3346 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)(162,163)(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)(178,179)(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)(192,193)(194,195)(196,197)(198,199)(200,201)(202,203)(204,205)(206,207)(208,209)(210,211)(212,213)(214,215)(216,217)(218,219)(220,221)(222,223)(224,225)(226,227)(228,229)(230,231)(232,233)(234,235)(236,237)(238,239)(240,241)(242,243)(244,245)(246,247)(248,249)(250,251)(252,253)(254,255)(256,257)(258,259)(260,261)(262,263)(264,265)(266,267)(268,269)(270,271)(272,273)(274,275)(276,277)(278,279)(280,281)(282,283)(284,285)(286,287)(288,289)(290,291)(292,293)(294,295)(296,297)(298,299)(300,301)(302,303)(304,305)(306,307)(308,309)(310,311)(312,313)(314,315)(316,317)(318,319)(320,321)(322,323)(324,325)(326,327)(328,329)(330,331)(332,333)(334,335)(336,337)(338,339)(340,341)(342,343)(344,345)(346,347)(348,349)(350,351)(352,353)(354,355)(356,357)(358,359)(360,361)(362,363)(364,365)(366,367)(368,369)(370,371)(372,373)(374,375)(376,377)(378,379)(380,381)(382,383)(384,385)(386,387)(388,389)(390,391)(392,393)(394,395)(396,397)(398,399)(400,401)(402,403)(404,405)(406,407)(408,409)(410,411)(412,413)(414,415)(416,417)(418,419)(420,421)(422,423)(424,425)(426,427)(428,429)(430,431)(432,433)(434,435)(436,437)(438,439)(440,441)(442,443)(444,445)(446,447)(448,449)(450,451)(452,453)(454,455)(456,457)(458,459)(460,461)(462,463)(464,465)(466,467)(468,469)(470,471)(472,473)(474,475)(476,477)(478,479)(480,481)(482,483)(484,485)(486,487)(488,489)(490,491)(492,493)(494,495)(496,497)(498,499)(500,501)(502,503)(504,505)(506,507)(508,509)(510,511)(512,513)(514,515)(516,517)(518,519)(520,521)(522,523)(524,525)(526,527)(528,529)(530,531)(532,533)(534,535)(536,537)(538,539)(540,541)(542,543)(544,545)(546,547)(548,549)(550,551)(552,553)(554,555)(556,557)(558,559)(560,561)(562,563)(564,565)(566,567)(568,569)(570,571)(572,573)(574,575)(576,577)(578,579)(580,581)(582,583)(584,585)(586,587)(588,589)(590,591)(592,593)(594,595)(596,597)(598,599)(600,601)(602,603)(604,605)(606,607)(608,609)(610,611)(612,613)(614,615)(616,617)(618,619)(620,621)(622,623)(624,625)(626,627)(628,629)(630,631)(632,633)(634,635)(636,637)(638,639)(640,641)(642,643)(644,645)(646,647)(648,649)(650,651)(652,653)(654,655)(656,657)(658,659)(660,661)(662,663)(664,665)(666,667)(668,669)(670,671)(672,673)(674,675)(676,677)(678,679)(680,681)(682,683)(684,685)(686,687)(688,689)(690,691)(692,693)(694,695)(696,697)(698,699)(700,701)(702,703)(704,705)(706,707)(708,709)(710,711)(712,713)(714,715)(716,717)(718,719)(720,721)(722,723)(724,725)(726,727)(728,729)(730,731)(732,733)(734,735)(736,737)(738,739)(740,741)(742,743)(744,745)(746,747)(748,749)(750,751)(752,753)(754,755)(756,757)(758,759)(760,761)(762,763)(764,765)(766,767)(768,769)(770,771)(772,773)(774,775)(776,777)(778,779)(780,781)(782,783)(784,785)(786,787)(788,789)(790,791)(792,793)(794,795)(796,797)(798,799)(800,801)(802,803)(804,805)(806,807)(808,809)(810,811)(812,813)(814,815)(816,817)(818,819)(820,821)(822,823)(824,825)(826,827)(828,829)(830,831)(832,833)(834,835)(836,837)(838,839)(840,841)(842,843)(844,845)(846,847)(848,849)(850,851)(852,853)(854,855)(856,857)(858,859)(860,861)(862,863)(864,865)(866,867)(868,869)(870,871)(872,873)(874,875)(876,877)(878,879)(880,881)(882,883)(884,885)(886,887)(888,889)(890,891)(892,893)(894,895)(896,897)(898,899)(900,901)(902,903)(904,905)(906,907)(908,909)(910,911)(912,913)(914,915)(916,917)(918,919)(920,921)(922,923)(924,925)(926,927)(928,929)(930,931)(932,933)(934,935)(936,937)(938,939)(940,941)(942,943)(944,945)(946,947)(948,949)(950,951)(952,953)(954,955)(956,957)(958,959)(960,961)(962,963)(964,965)(966,967)(968,969)(970,971)(972,973)(974,975)(976,977)(978,979)(980,981)(982,983)(984,985)(986,987)(988,989)(990,991)(992,993)(994,995)(996,997)(998,999)(1000,1001)(1002,1003)(1004,1005)(1006,1007)(1008,1009)(1010,1011)(1012,1013)(1014,1015)(1016,1017)(1018,1019)(1020,1021)(1022,1023)(1024,1025)(1026,1027)(1028,1029)(1030,1031)(1032,1033)(1034,1035)(1036,1037)(1038,1039)(1040,1041)(1042,1043)(1044,1045)(1046,1047)(1048,1049)(1050,1051)(1052,1053)(1054,1055)(1056,1057)(1058,1059)(1060,1061)(1062,1063)(1064,1065)(1066,1067)(1068,1069)(1070,1071)(1072,1073)(1074,1075)(1076,1077)(1078,1079)(1080,1081)(1082,1083)(1084,1085)(1086,1087)(1088,1089)(1090,1091)(1092,1093)(1094,1095)(1096,1097)(1098,1099)(1100,1101)(1102,1103)(1104,1105)(1106,1107)(1108,1109)(1110,1111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1383,1381,1379,1377,1375,1373,1371,1369,1367,1365,1363,1361,1359,1357,1355,1353,1351,1349,1347,1345,1343,1341,1339,1337,1335,1333,1331,1329,1327,1325,1323,1321,1319,1317,1315,1313,1311,1309,1307,1305,1303,1301,1299,1297,1295,1293,1291,1289,1287,1285,1283,1281,1279,1277,1275,1273,1271,1269,1267,1265,1263,1261,1259,1257,1255,1253,1251,1249,1247,1245,1243,1241,1239,1237,1235,1233,1231,1229,1227,1225,1223,1221,1219,1217,1215,1213,1211,1209,1207,1205,1203,1201,1199,1197,1195,1193,1191,1189,1187,1185,1183,1181,1179,1177,1175,1173,1171,1169,1167,1165,1163,1161,1159,1157,1155,1153,1151,1149,1147,1145,1143,1141,1139,1137,1135,1133,1131,1129,1127,1125,1123,1121,1119,1117,1115,1113,1111,1109,1107,1105,1103,1101,1099,1097,1095,1093,1091,1089,1087,1085,1083,1081,1079,1077,1075,1073,1071,1069,1067,1065,1063,1061,1059,1057,1055,1053,1051,1049,1047,1045,1043,1041,1039,1037,1035,1033,1031,1029,1027,1025,1023,1021,1019,1017,1015,1013,1011,1009,1007,1005,1003,1001,999,997,995,993,991,989,987,985,983,981,979,977,975,973,971,969,967,965,963,961,959,957,955,953,951,949,947,945,943,941,939,937,935,933,931,929,927,925,923,921,919,917,915,913,911,909,907,905,903,901,899,897,895,893,891,889,887,885,883,881,879,877,875,873,871,869,867,865,863,861,859,857,855,853,851,849,847,845,843,841,839,837,835,833,831,829,827,825,823,821,819,817,815,813,811,809,807,805,803,801,799,797,795,793,791,789,787,785,783,781,779,777,775,773,771,769,767,765,763,761,759,757,755,753,751,749,747,745,743,741,739,737,735,733,731,729,727,725,723,721,719,717,715,713,711,709,707,705,703,701,699,697,695,693,691,689,687,685,683,681,679,677,675,673,671,669,667,665,663,661,659,657,655,653,651,649,647,645,643,641,639,637,635,633,631,629,627,625,623,621,619,617,615,613,611,609,607,605,603,601,599,597,595,593,591,589,587,585,583,581,579,577,575,573,571,569,567,565,563,561,559,557,555,553,551,549,547,545,543,541,539,537,535,533,531,529,527,525,523,521,519,517,515,513,511,509,507,505,503,501,499,497,495,493,491,489,487,485,483,481,479,477,475,473,471,469,467,465,463,461,459,457,455,453,451,449,447,445,443,441,439,437,435,433,431,429,427,425,423,421,419,417,415,413,411,409,407,405,403,401,399,397,395,393,391,389,387,385,383,381,379,377,375,373,371,369,367,365,363,361,359,357,355,353,351,349,347,345,343,341,339,337,335,333,331,329,327,325,323,321,319,317,315,313,311,309,307,305,303,301,299,297,295,293,291,289,287,285,283,281,279,277,275,273,271,269,267,265,263,261,259,257,255,253,251,249,247,245,243,241,239,237,235,233,231,229,227,225,223,221,219,217,215,213,211,209,207,205,203,201,199,197,195,193,191,189,187,185,183,181,179,177,175,173,171,169,167,165,163,161,159,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)
Conjugacy classes & character table
5019 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20058, 4);
Finite Group Databasebeta