D₂₉₈₃₇ #68712905

order	59674
automorphism	Aut(G) order 890216732
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₉₈₃₇

Splittings

Fitting, socle, derived, Sylow

C₂₉₈₃₇ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉₈₃₇	C₂
LCS	G ▷ C₂₉₈₃₇
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29837
transitive degree	μ_t(G) = 29837

A minimal faithful permutation representation — 2 generators on 29837 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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362)(14478,15361)(14479,15360)(14480,15359)(14481,15358)(14482,15357)(14483,15356)(14484,15355)(14485,15354)(14486,15353)(14487,15352)(14488,15351)(14489,15350)(14490,15349)(14491,15348)(14492,15347)(14493,15346)(14494,15345)(14495,15344)(14496,15343)(14497,15342)(14498,15341)(14499,15340)(14500,15339)(14501,15338)(14502,15337)(14503,15336)(14504,15335)(14505,15334)(14506,15333)(14507,15332)(14508,15331)(14509,15330)(14510,15329)(14511,15328)(14512,15327)(14513,15326)(14514,15325)(14515,15324)(14516,15323)(14517,15322)(14518,15321)(14519,15320)(14520,15319)(14521,15318)(14522,15317)(14523,15316)(14524,15315)(14525,15314)(14526,15313)(14527,15312)(14528,15311)(14529,15310)(14530,15309)(14531,15308)(14532,15307)(14533,15306)(14534,15305)(14535,15304)(14536,15303)(14537,15302)(14538,15301)(14539,15300)(14540,15299)(14541,15298)(14542,15297)(14543,15296)(14544,15295)(14545,15294)(14546,15293)(14547,15292)(14548,15291)(14549,15290)(14550,15289)(14551,15288)(14552,15287)(14553,15286)(14554,15285)(14555,15284)(14556,15283)(14557,15282)(14558,15281)(14559,15280)(14560,15279)(14561,15278)(14562,15277)(14563,15276)(14564,15275)(14565,15274)(14566,15273)(14567,15272)(14568,15271)(14569,15270)(14570,15269)(14571,15268)(14572,15267)(14573,15266)(14574,15265)(14575,15264)(14576,15263)(14577,15262)(14578,15261)(14579,15260)(14580,15259)(14581,15258)(14582,15257)(14583,15256)(14584,15255)(14585,15254)(14586,15253)(14587,15252)(14588,15251)(14589,15250)(14590,15249)(14591,15248)(14592,15247)(14593,15246)(14594,15245)(14595,15244)(14596,15243)(14597,15242)(14598,15241)(14599,15240)(14600,15239)(14601,15238)(14602,15237)(14603,15236)(14604,15235)(14605,15234)(14606,15233)(14607,15232)(14608,15231)(14609,15230)(14610,15229)(14611,15228)(14612,15227)(14613,15226)(14614,15225)(14615,15224)(14616,15223)(14617,15222)(14618,15221)(14619,15220)(14620,15219)(14621,15218)(14622,15217)(14623,15216)(14624,15215)(14625,15214)(14626,15213)(14627,15212)(14628,15211)(14629,15210)(14630,15209)(14631,15208)(14632,15207)(14633,15206)(14634,15205)(14635,15204)(14636,15203)(14637,15202)(14638,15201)(14639,15200)(14640,15199)(14641,15198)(14642,15197)(14643,15196)(14644,15195)(14645,15194)(14646,15193)(14647,15192)(14648,15191)(14649,15190)(14650,15189)(14651,15188)(14652,15187)(14653,15186)(14654,15185)(14655,15184)(14656,15183)(14657,15182)(14658,15181)(14659,15180)(14660,15179)(14661,15178)(14662,15177)(14663,15176)(14664,15175)(14665,15174)(14666,15173)(14667,15172)(14668,15171)(14669,15170)(14670,15169)(14671,15168)(14672,15167)(14673,15166)(14674,15165)(14675,15164)(14676,15163)(14677,15162)(14678,15161)(14679,15160)(14680,15159)(14681,15158)(14682,15157)(14683,15156)(14684,15155)(14685,15154)(14686,15153)(14687,15152)(14688,15151)(14689,15150)(14690,15149)(14691,15148)(14692,15147)(14693,15146)(14694,15145)(14695,15144)(14696,15143)(14697,15142)(14698,15141)(14699,15140)(14700,15139)(14701,15138)(14702,15137)(14703,15136)(14704,15135)(14705,15134)(14706,15133)(14707,15132)(14708,15131)(14709,15130)(14710,15129)(14711,15128)(14712,15127)(14713,15126)(14714,15125)(14715,15124)(14716,15123)(14717,15122)(14718,15121)(14719,15120)(14720,15119)(14721,15118)(14722,15117)(14723,15116)(14724,15115)(14725,15114)(14726,15113)(14727,15112)(14728,15111)(14729,15110)(14730,15109)(14731,15108)(14732,15107)(14733,15106)(14734,15105)(14735,15104)(14736,15103)(14737,15102)(14738,15101)(14739,15100)(14740,15099)(14741,15098)(14742,15097)(14743,15096)(14744,15095)(14745,15094)(14746,15093)(14747,15092)(14748,15091)(14749,15090)(14750,15089)(14751,15088)(14752,15087)(14753,15086)(14754,15085)(14755,15084)(14756,15083)(14757,15082)(14758,15081)(14759,15080)(14760,15079)(14761,15078)(14762,15077)(14763,15076)(14764,15075)(14765,15074)(14766,15073)(14767,15072)(14768,15071)(14769,15070)(14770,15069)(14771,15068)(14772,15067)(14773,15066)(14774,15065)(14775,15064)(14776,15063)(14777,15062)(14778,15061)(14779,15060)(14780,15059)(14781,15058)(14782,15057)(14783,15056)(14784,15055)(14785,15054)(14786,15053)(14787,15052)(14788,15051)(14789,15050)(14790,15049)(14791,15048)(14792,15047)(14793,15046)(14794,15045)(14795,15044)(14796,15043)(14797,15042)(14798,15041)(14799,15040)(14800,15039)(14801,15038)(14802,15037)(14803,15036)(14804,15035)(14805,15034)(14806,15033)(14807,15032)(14808,15031)(14809,15030)(14810,15029)(14811,15028)(14812,15027)(14813,15026)(14814,15025)(14815,15024)(14816,15023)(14817,15022)(14818,15021)(14819,15020)(14820,15019)(14821,15018)(14822,15017)(14823,15016)(14824,15015)(14825,15014)(14826,15013)(14827,15012)(14828,15011)(14829,15010)(14830,15009)(14831,15008)(14832,15007)(14833,15006)(14834,15005)(14835,15004)(14836,15003)(14837,15002)(14838,15001)(14839,15000)(14840,14999)(14841,14998)(14842,14997)(14843,14996)(14844,14995)(14845,14994)(14846,14993)(14847,14992)(14848,14991)(14849,14990)(14850,14989)(14851,14988)(14852,14987)(14853,14986)(14854,14985)(14855,14984)(14856,14983)(14857,14982)(14858,14981)(14859,14980)(14860,14979)(14861,14978)(14862,14977)(14863,14976)(14864,14975)(14865,14974)(14866,14973)(14867,14972)(14868,14971)(14869,14970)(14870,14969)(14871,14968)(14872,14967)(14873,14966)(14874,14965)(14875,14964)(14876,14963)(14877,14962)(14878,14961)(14879,14960)(14880,14959)(14881,14958)(14882,14957)(14883,14956)(14884,14955)(14885,14954)(14886,14953)(14887,14952)(14888,14951)(14889,14950)(14890,14949)(14891,14948)(14892,14947)(14893,14946)(14894,14945)(14895,14944)(14896,14943)(14897,14942)(14898,14941)(14899,14940)(14900,14939)(14901,14938)(14902,14937)(14903,14936)(14904,14935)(14905,14934)(14906,14933)(14907,14932)(14908,14931)(14909,14930)(14910,14929)(14911,14928)(14912,14927)(14913,14926)(14914,14925)(14915,14924)(14916,14923)(14917,14922)(14918,14921)(14919,14920)

Polycyclic presentation:

2,29837|b^a=b^29836

Conjugacy classes & character table

14920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(59674, 1);

D29837 #68712905