D₂₉₄₃₇ #67548726

order	58874
automorphism	Aut(G) order 866507532
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₉₄₃₇

Splittings

Fitting, socle, derived, Sylow

C₂₉₄₃₇ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉₄₃₇	C₂
LCS	G ▷ C₂₉₄₃₇
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29437
transitive degree	μ_t(G) = 29437

A minimal faithful permutation representation — 2 generators on 29437 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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162)(14278,15161)(14279,15160)(14280,15159)(14281,15158)(14282,15157)(14283,15156)(14284,15155)(14285,15154)(14286,15153)(14287,15152)(14288,15151)(14289,15150)(14290,15149)(14291,15148)(14292,15147)(14293,15146)(14294,15145)(14295,15144)(14296,15143)(14297,15142)(14298,15141)(14299,15140)(14300,15139)(14301,15138)(14302,15137)(14303,15136)(14304,15135)(14305,15134)(14306,15133)(14307,15132)(14308,15131)(14309,15130)(14310,15129)(14311,15128)(14312,15127)(14313,15126)(14314,15125)(14315,15124)(14316,15123)(14317,15122)(14318,15121)(14319,15120)(14320,15119)(14321,15118)(14322,15117)(14323,15116)(14324,15115)(14325,15114)(14326,15113)(14327,15112)(14328,15111)(14329,15110)(14330,15109)(14331,15108)(14332,15107)(14333,15106)(14334,15105)(14335,15104)(14336,15103)(14337,15102)(14338,15101)(14339,15100)(14340,15099)(14341,15098)(14342,15097)(14343,15096)(14344,15095)(14345,15094)(14346,15093)(14347,15092)(14348,15091)(14349,15090)(14350,15089)(14351,15088)(14352,15087)(14353,15086)(14354,15085)(14355,15084)(14356,15083)(14357,15082)(14358,15081)(14359,15080)(14360,15079)(14361,15078)(14362,15077)(14363,15076)(14364,15075)(14365,15074)(14366,15073)(14367,15072)(14368,15071)(14369,15070)(14370,15069)(14371,15068)(14372,15067)(14373,15066)(14374,15065)(14375,15064)(14376,15063)(14377,15062)(14378,15061)(14379,15060)(14380,15059)(14381,15058)(14382,15057)(14383,15056)(14384,15055)(14385,15054)(14386,15053)(14387,15052)(14388,15051)(14389,15050)(14390,15049)(14391,15048)(14392,15047)(14393,15046)(14394,15045)(14395,15044)(14396,15043)(14397,15042)(14398,15041)(14399,15040)(14400,15039)(14401,15038)(14402,15037)(14403,15036)(14404,15035)(14405,15034)(14406,15033)(14407,15032)(14408,15031)(14409,15030)(14410,15029)(14411,15028)(14412,15027)(14413,15026)(14414,15025)(14415,15024)(14416,15023)(14417,15022)(14418,15021)(14419,15020)(14420,15019)(14421,15018)(14422,15017)(14423,15016)(14424,15015)(14425,15014)(14426,15013)(14427,15012)(14428,15011)(14429,15010)(14430,15009)(14431,15008)(14432,15007)(14433,15006)(14434,15005)(14435,15004)(14436,15003)(14437,15002)(14438,15001)(14439,15000)(14440,14999)(14441,14998)(14442,14997)(14443,14996)(14444,14995)(14445,14994)(14446,14993)(14447,14992)(14448,14991)(14449,14990)(14450,14989)(14451,14988)(14452,14987)(14453,14986)(14454,14985)(14455,14984)(14456,14983)(14457,14982)(14458,14981)(14459,14980)(14460,14979)(14461,14978)(14462,14977)(14463,14976)(14464,14975)(14465,14974)(14466,14973)(14467,14972)(14468,14971)(14469,14970)(14470,14969)(14471,14968)(14472,14967)(14473,14966)(14474,14965)(14475,14964)(14476,14963)(14477,14962)(14478,14961)(14479,14960)(14480,14959)(14481,14958)(14482,14957)(14483,14956)(14484,14955)(14485,14954)(14486,14953)(14487,14952)(14488,14951)(14489,14950)(14490,14949)(14491,14948)(14492,14947)(14493,14946)(14494,14945)(14495,14944)(14496,14943)(14497,14942)(14498,14941)(14499,14940)(14500,14939)(14501,14938)(14502,14937)(14503,14936)(14504,14935)(14505,14934)(14506,14933)(14507,14932)(14508,14931)(14509,14930)(14510,14929)(14511,14928)(14512,14927)(14513,14926)(14514,14925)(14515,14924)(14516,14923)(14517,14922)(14518,14921)(14519,14920)(14520,14919)(14521,14918)(14522,14917)(14523,14916)(14524,14915)(14525,14914)(14526,14913)(14527,14912)(14528,14911)(14529,14910)(14530,14909)(14531,14908)(14532,14907)(14533,14906)(14534,14905)(14535,14904)(14536,14903)(14537,14902)(14538,14901)(14539,14900)(14540,14899)(14541,14898)(14542,14897)(14543,14896)(14544,14895)(14545,14894)(14546,14893)(14547,14892)(14548,14891)(14549,14890)(14550,14889)(14551,14888)(14552,14887)(14553,14886)(14554,14885)(14555,14884)(14556,14883)(14557,14882)(14558,14881)(14559,14880)(14560,14879)(14561,14878)(14562,14877)(14563,14876)(14564,14875)(14565,14874)(14566,14873)(14567,14872)(14568,14871)(14569,14870)(14570,14869)(14571,14868)(14572,14867)(14573,14866)(14574,14865)(14575,14864)(14576,14863)(14577,14862)(14578,14861)(14579,14860)(14580,14859)(14581,14858)(14582,14857)(14583,14856)(14584,14855)(14585,14854)(14586,14853)(14587,14852)(14588,14851)(14589,14850)(14590,14849)(14591,14848)(14592,14847)(14593,14846)(14594,14845)(14595,14844)(14596,14843)(14597,14842)(14598,14841)(14599,14840)(14600,14839)(14601,14838)(14602,14837)(14603,14836)(14604,14835)(14605,14834)(14606,14833)(14607,14832)(14608,14831)(14609,14830)(14610,14829)(14611,14828)(14612,14827)(14613,14826)(14614,14825)(14615,14824)(14616,14823)(14617,14822)(14618,14821)(14619,14820)(14620,14819)(14621,14818)(14622,14817)(14623,14816)(14624,14815)(14625,14814)(14626,14813)(14627,14812)(14628,14811)(14629,14810)(14630,14809)(14631,14808)(14632,14807)(14633,14806)(14634,14805)(14635,14804)(14636,14803)(14637,14802)(14638,14801)(14639,14800)(14640,14799)(14641,14798)(14642,14797)(14643,14796)(14644,14795)(14645,14794)(14646,14793)(14647,14792)(14648,14791)(14649,14790)(14650,14789)(14651,14788)(14652,14787)(14653,14786)(14654,14785)(14655,14784)(14656,14783)(14657,14782)(14658,14781)(14659,14780)(14660,14779)(14661,14778)(14662,14777)(14663,14776)(14664,14775)(14665,14774)(14666,14773)(14667,14772)(14668,14771)(14669,14770)(14670,14769)(14671,14768)(14672,14767)(14673,14766)(14674,14765)(14675,14764)(14676,14763)(14677,14762)(14678,14761)(14679,14760)(14680,14759)(14681,14758)(14682,14757)(14683,14756)(14684,14755)(14685,14754)(14686,14753)(14687,14752)(14688,14751)(14689,14750)(14690,14749)(14691,14748)(14692,14747)(14693,14746)(14694,14745)(14695,14744)(14696,14743)(14697,14742)(14698,14741)(14699,14740)(14700,14739)(14701,14738)(14702,14737)(14703,14736)(14704,14735)(14705,14734)(14706,14733)(14707,14732)(14708,14731)(14709,14730)(14710,14729)(14711,14728)(14712,14727)(14713,14726)(14714,14725)(14715,14724)(14716,14723)(14717,14722)(14718,14721)(14719,14720)

Polycyclic presentation:

2,29437|b^a=b^29436

Conjugacy classes & character table

14720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(58874, 1);

D29437 #67548726