D₂₉₉₈₉ #68735487

order	59978
automorphism	Aut(G) order 899310132
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₉₉₈₉

Splittings

Fitting, socle, derived, Sylow

C₂₉₉₈₉ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉₉₈₉	C₂
LCS	G ▷ C₂₉₉₈₉
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29989
transitive degree	μ_t(G) = 29989

A minimal faithful permutation representation — 2 generators on 29989 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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15584)(14408,15583)(14409,15582)(14410,15581)(14411,15580)(14412,15579)(14413,15578)(14414,15577)(14415,15576)(14416,15575)(14417,15574)(14418,15573)(14419,15572)(14420,15571)(14421,15570)(14422,15569)(14423,15568)(14424,15567)(14425,15566)(14426,15565)(14427,15564)(14428,15563)(14429,15562)(14430,15561)(14431,15560)(14432,15559)(14433,15558)(14434,15557)(14435,15556)(14436,15555)(14437,15554)(14438,15553)(14439,15552)(14440,15551)(14441,15550)(14442,15549)(14443,15548)(14444,15547)(14445,15546)(14446,15545)(14447,15544)(14448,15543)(14449,15542)(14450,15541)(14451,15540)(14452,15539)(14453,15538)(14454,15537)(14455,15536)(14456,15535)(14457,15534)(14458,15533)(14459,15532)(14460,15531)(14461,15530)(14462,15529)(14463,15528)(14464,15527)(14465,15526)(14466,15525)(14467,15524)(14468,15523)(14469,15522)(14470,15521)(14471,15520)(14472,15519)(14473,15518)(14474,15517)(14475,15516)(14476,15515)(14477,15514)(14478,15513)(14479,15512)(14480,15511)(14481,15510)(14482,15509)(14483,15508)(14484,15507)(14485,15506)(14486,15505)(14487,15504)(14488,15503)(14489,15502)(14490,15501)(14491,15500)(14492,15499)(14493,15498)(14494,15497)(14495,15496)(14496,15495)(14497,15494)(14498,15493)(14499,15492)(14500,15491)(14501,15490)(14502,15489)(14503,15488)(14504,15487)(14505,15486)(14506,15485)(14507,15484)(14508,15483)(14509,15482)(14510,15481)(14511,15480)(14512,15479)(14513,15478)(14514,15477)(14515,15476)(14516,15475)(14517,15474)(14518,15473)(14519,15472)(14520,15471)(14521,15470)(14522,15469)(14523,15468)(14524,15467)(14525,15466)(14526,15465)(14527,15464)(14528,15463)(14529,15462)(14530,15461)(14531,15460)(14532,15459)(14533,15458)(14534,15457)(14535,15456)(14536,15455)(14537,15454)(14538,15453)(14539,15452)(14540,15451)(14541,15450)(14542,15449)(14543,15448)(14544,15447)(14545,15446)(14546,15445)(14547,15444)(14548,15443)(14549,15442)(14550,15441)(14551,15440)(14552,15439)(14553,15438)(14554,15437)(14555,15436)(14556,15435)(14557,15434)(14558,15433)(14559,15432)(14560,15431)(14561,15430)(14562,15429)(14563,15428)(14564,15427)(14565,15426)(14566,15425)(14567,15424)(14568,15423)(14569,15422)(14570,15421)(14571,15420)(14572,15419)(14573,15418)(14574,15417)(14575,15416)(14576,15415)(14577,15414)(14578,15413)(14579,15412)(14580,15411)(14581,15410)(14582,15409)(14583,15408)(14584,15407)(14585,15406)(14586,15405)(14587,15404)(14588,15403)(14589,15402)(14590,15401)(14591,15400)(14592,15399)(14593,15398)(14594,15397)(14595,15396)(14596,15395)(14597,15394)(14598,15393)(14599,15392)(14600,15391)(14601,15390)(14602,15389)(14603,15388)(14604,15387)(14605,15386)(14606,15385)(14607,15384)(14608,15383)(14609,15382)(14610,15381)(14611,15380)(14612,15379)(14613,15378)(14614,15377)(14615,15376)(14616,15375)(14617,15374)(14618,15373)(14619,15372)(14620,15371)(14621,15370)(14622,15369)(14623,15368)(14624,15367)(14625,15366)(14626,15365)(14627,15364)(14628,15363)(14629,15362)(14630,15361)(14631,15360)(14632,15359)(14633,15358)(14634,15357)(14635,15356)(14636,15355)(14637,15354)(14638,15353)(14639,15352)(14640,15351)(14641,15350)(14642,15349)(14643,15348)(14644,15347)(14645,15346)(14646,15345)(14647,15344)(14648,15343)(14649,15342)(14650,15341)(14651,15340)(14652,15339)(14653,15338)(14654,15337)(14655,15336)(14656,15335)(14657,15334)(14658,15333)(14659,15332)(14660,15331)(14661,15330)(14662,15329)(14663,15328)(14664,15327)(14665,15326)(14666,15325)(14667,15324)(14668,15323)(14669,15322)(14670,15321)(14671,15320)(14672,15319)(14673,15318)(14674,15317)(14675,15316)(14676,15315)(14677,15314)(14678,15313)(14679,15312)(14680,15311)(14681,15310)(14682,15309)(14683,15308)(14684,15307)(14685,15306)(14686,15305)(14687,15304)(14688,15303)(14689,15302)(14690,15301)(14691,15300)(14692,15299)(14693,15298)(14694,15297)(14695,15296)(14696,15295)(14697,15294)(14698,15293)(14699,15292)(14700,15291)(14701,15290)(14702,15289)(14703,15288)(14704,15287)(14705,15286)(14706,15285)(14707,15284)(14708,15283)(14709,15282)(14710,15281)(14711,15280)(14712,15279)(14713,15278)(14714,15277)(14715,15276)(14716,15275)(14717,15274)(14718,15273)(14719,15272)(14720,15271)(14721,15270)(14722,15269)(14723,15268)(14724,15267)(14725,15266)(14726,15265)(14727,15264)(14728,15263)(14729,15262)(14730,15261)(14731,15260)(14732,15259)(14733,15258)(14734,15257)(14735,15256)(14736,15255)(14737,15254)(14738,15253)(14739,15252)(14740,15251)(14741,15250)(14742,15249)(14743,15248)(14744,15247)(14745,15246)(14746,15245)(14747,15244)(14748,15243)(14749,15242)(14750,15241)(14751,15240)(14752,15239)(14753,15238)(14754,15237)(14755,15236)(14756,15235)(14757,15234)(14758,15233)(14759,15232)(14760,15231)(14761,15230)(14762,15229)(14763,15228)(14764,15227)(14765,15226)(14766,15225)(14767,15224)(14768,15223)(14769,15222)(14770,15221)(14771,15220)(14772,15219)(14773,15218)(14774,15217)(14775,15216)(14776,15215)(14777,15214)(14778,15213)(14779,15212)(14780,15211)(14781,15210)(14782,15209)(14783,15208)(14784,15207)(14785,15206)(14786,15205)(14787,15204)(14788,15203)(14789,15202)(14790,15201)(14791,15200)(14792,15199)(14793,15198)(14794,15197)(14795,15196)(14796,15195)(14797,15194)(14798,15193)(14799,15192)(14800,15191)(14801,15190)(14802,15189)(14803,15188)(14804,15187)(14805,15186)(14806,15185)(14807,15184)(14808,15183)(14809,15182)(14810,15181)(14811,15180)(14812,15179)(14813,15178)(14814,15177)(14815,15176)(14816,15175)(14817,15174)(14818,15173)(14819,15172)(14820,15171)(14821,15170)(14822,15169)(14823,15168)(14824,15167)(14825,15166)(14826,15165)(14827,15164)(14828,15163)(14829,15162)(14830,15161)(14831,15160)(14832,15159)(14833,15158)(14834,15157)(14835,15156)(14836,15155)(14837,15154)(14838,15153)(14839,15152)(14840,15151)(14841,15150)(14842,15149)(14843,15148)(14844,15147)(14845,15146)(14846,15145)(14847,15144)(14848,15143)(14849,15142)(14850,15141)(14851,15140)(14852,15139)(14853,15138)(14854,15137)(14855,15136)(14856,15135)(14857,15134)(14858,15133)(14859,15132)(14860,15131)(14861,15130)(14862,15129)(14863,15128)(14864,15127)(14865,15126)(14866,15125)(14867,15124)(14868,15123)(14869,15122)(14870,15121)(14871,15120)(14872,15119)(14873,15118)(14874,15117)(14875,15116)(14876,15115)(14877,15114)(14878,15113)(14879,15112)(14880,15111)(14881,15110)(14882,15109)(14883,15108)(14884,15107)(14885,15106)(14886,15105)(14887,15104)(14888,15103)(14889,15102)(14890,15101)(14891,15100)(14892,15099)(14893,15098)(14894,15097)(14895,15096)(14896,15095)(14897,15094)(14898,15093)(14899,15092)(14900,15091)(14901,15090)(14902,15089)(14903,15088)(14904,15087)(14905,15086)(14906,15085)(14907,15084)(14908,15083)(14909,15082)(14910,15081)(14911,15080)(14912,15079)(14913,15078)(14914,15077)(14915,15076)(14916,15075)(14917,15074)(14918,15073)(14919,15072)(14920,15071)(14921,15070)(14922,15069)(14923,15068)(14924,15067)(14925,15066)(14926,15065)(14927,15064)(14928,15063)(14929,15062)(14930,15061)(14931,15060)(14932,15059)(14933,15058)(14934,15057)(14935,15056)(14936,15055)(14937,15054)(14938,15053)(14939,15052)(14940,15051)(14941,15050)(14942,15049)(14943,15048)(14944,15047)(14945,15046)(14946,15045)(14947,15044)(14948,15043)(14949,15042)(14950,15041)(14951,15040)(14952,15039)(14953,15038)(14954,15037)(14955,15036)(14956,15035)(14957,15034)(14958,15033)(14959,15032)(14960,15031)(14961,15030)(14962,15029)(14963,15028)(14964,15027)(14965,15026)(14966,15025)(14967,15024)(14968,15023)(14969,15022)(14970,15021)(14971,15020)(14972,15019)(14973,15018)(14974,15017)(14975,15016)(14976,15015)(14977,15014)(14978,15013)(14979,15012)(14980,15011)(14981,15010)(14982,15009)(14983,15008)(14984,15007)(14985,15006)(14986,15005)(14987,15004)(14988,15003)(14989,15002)(14990,15001)(14991,15000)(14992,14999)(14993,14998)(14994,14997)(14995,14996)

Polycyclic presentation:

2,29989|b^a=b^29988

Conjugacy classes & character table

14996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(59978, 1);

D29989 #68735487