D₂₉₈₆₃ #68713007

order	59726
automorphism	Aut(G) order 891768906
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₉₈₆₃

Splittings

Fitting, socle, derived, Sylow

C₂₉₈₆₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉₈₆₃	C₂
LCS	G ▷ C₂₉₈₆₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29863
transitive degree	μ_t(G) = 29863

A minimal faithful permutation representation — 2 generators on 29863 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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400)(14466,15399)(14467,15398)(14468,15397)(14469,15396)(14470,15395)(14471,15394)(14472,15393)(14473,15392)(14474,15391)(14475,15390)(14476,15389)(14477,15388)(14478,15387)(14479,15386)(14480,15385)(14481,15384)(14482,15383)(14483,15382)(14484,15381)(14485,15380)(14486,15379)(14487,15378)(14488,15377)(14489,15376)(14490,15375)(14491,15374)(14492,15373)(14493,15372)(14494,15371)(14495,15370)(14496,15369)(14497,15368)(14498,15367)(14499,15366)(14500,15365)(14501,15364)(14502,15363)(14503,15362)(14504,15361)(14505,15360)(14506,15359)(14507,15358)(14508,15357)(14509,15356)(14510,15355)(14511,15354)(14512,15353)(14513,15352)(14514,15351)(14515,15350)(14516,15349)(14517,15348)(14518,15347)(14519,15346)(14520,15345)(14521,15344)(14522,15343)(14523,15342)(14524,15341)(14525,15340)(14526,15339)(14527,15338)(14528,15337)(14529,15336)(14530,15335)(14531,15334)(14532,15333)(14533,15332)(14534,15331)(14535,15330)(14536,15329)(14537,15328)(14538,15327)(14539,15326)(14540,15325)(14541,15324)(14542,15323)(14543,15322)(14544,15321)(14545,15320)(14546,15319)(14547,15318)(14548,15317)(14549,15316)(14550,15315)(14551,15314)(14552,15313)(14553,15312)(14554,15311)(14555,15310)(14556,15309)(14557,15308)(14558,15307)(14559,15306)(14560,15305)(14561,15304)(14562,15303)(14563,15302)(14564,15301)(14565,15300)(14566,15299)(14567,15298)(14568,15297)(14569,15296)(14570,15295)(14571,15294)(14572,15293)(14573,15292)(14574,15291)(14575,15290)(14576,15289)(14577,15288)(14578,15287)(14579,15286)(14580,15285)(14581,15284)(14582,15283)(14583,15282)(14584,15281)(14585,15280)(14586,15279)(14587,15278)(14588,15277)(14589,15276)(14590,15275)(14591,15274)(14592,15273)(14593,15272)(14594,15271)(14595,15270)(14596,15269)(14597,15268)(14598,15267)(14599,15266)(14600,15265)(14601,15264)(14602,15263)(14603,15262)(14604,15261)(14605,15260)(14606,15259)(14607,15258)(14608,15257)(14609,15256)(14610,15255)(14611,15254)(14612,15253)(14613,15252)(14614,15251)(14615,15250)(14616,15249)(14617,15248)(14618,15247)(14619,15246)(14620,15245)(14621,15244)(14622,15243)(14623,15242)(14624,15241)(14625,15240)(14626,15239)(14627,15238)(14628,15237)(14629,15236)(14630,15235)(14631,15234)(14632,15233)(14633,15232)(14634,15231)(14635,15230)(14636,15229)(14637,15228)(14638,15227)(14639,15226)(14640,15225)(14641,15224)(14642,15223)(14643,15222)(14644,15221)(14645,15220)(14646,15219)(14647,15218)(14648,15217)(14649,15216)(14650,15215)(14651,15214)(14652,15213)(14653,15212)(14654,15211)(14655,15210)(14656,15209)(14657,15208)(14658,15207)(14659,15206)(14660,15205)(14661,15204)(14662,15203)(14663,15202)(14664,15201)(14665,15200)(14666,15199)(14667,15198)(14668,15197)(14669,15196)(14670,15195)(14671,15194)(14672,15193)(14673,15192)(14674,15191)(14675,15190)(14676,15189)(14677,15188)(14678,15187)(14679,15186)(14680,15185)(14681,15184)(14682,15183)(14683,15182)(14684,15181)(14685,15180)(14686,15179)(14687,15178)(14688,15177)(14689,15176)(14690,15175)(14691,15174)(14692,15173)(14693,15172)(14694,15171)(14695,15170)(14696,15169)(14697,15168)(14698,15167)(14699,15166)(14700,15165)(14701,15164)(14702,15163)(14703,15162)(14704,15161)(14705,15160)(14706,15159)(14707,15158)(14708,15157)(14709,15156)(14710,15155)(14711,15154)(14712,15153)(14713,15152)(14714,15151)(14715,15150)(14716,15149)(14717,15148)(14718,15147)(14719,15146)(14720,15145)(14721,15144)(14722,15143)(14723,15142)(14724,15141)(14725,15140)(14726,15139)(14727,15138)(14728,15137)(14729,15136)(14730,15135)(14731,15134)(14732,15133)(14733,15132)(14734,15131)(14735,15130)(14736,15129)(14737,15128)(14738,15127)(14739,15126)(14740,15125)(14741,15124)(14742,15123)(14743,15122)(14744,15121)(14745,15120)(14746,15119)(14747,15118)(14748,15117)(14749,15116)(14750,15115)(14751,15114)(14752,15113)(14753,15112)(14754,15111)(14755,15110)(14756,15109)(14757,15108)(14758,15107)(14759,15106)(14760,15105)(14761,15104)(14762,15103)(14763,15102)(14764,15101)(14765,15100)(14766,15099)(14767,15098)(14768,15097)(14769,15096)(14770,15095)(14771,15094)(14772,15093)(14773,15092)(14774,15091)(14775,15090)(14776,15089)(14777,15088)(14778,15087)(14779,15086)(14780,15085)(14781,15084)(14782,15083)(14783,15082)(14784,15081)(14785,15080)(14786,15079)(14787,15078)(14788,15077)(14789,15076)(14790,15075)(14791,15074)(14792,15073)(14793,15072)(14794,15071)(14795,15070)(14796,15069)(14797,15068)(14798,15067)(14799,15066)(14800,15065)(14801,15064)(14802,15063)(14803,15062)(14804,15061)(14805,15060)(14806,15059)(14807,15058)(14808,15057)(14809,15056)(14810,15055)(14811,15054)(14812,15053)(14813,15052)(14814,15051)(14815,15050)(14816,15049)(14817,15048)(14818,15047)(14819,15046)(14820,15045)(14821,15044)(14822,15043)(14823,15042)(14824,15041)(14825,15040)(14826,15039)(14827,15038)(14828,15037)(14829,15036)(14830,15035)(14831,15034)(14832,15033)(14833,15032)(14834,15031)(14835,15030)(14836,15029)(14837,15028)(14838,15027)(14839,15026)(14840,15025)(14841,15024)(14842,15023)(14843,15022)(14844,15021)(14845,15020)(14846,15019)(14847,15018)(14848,15017)(14849,15016)(14850,15015)(14851,15014)(14852,15013)(14853,15012)(14854,15011)(14855,15010)(14856,15009)(14857,15008)(14858,15007)(14859,15006)(14860,15005)(14861,15004)(14862,15003)(14863,15002)(14864,15001)(14865,15000)(14866,14999)(14867,14998)(14868,14997)(14869,14996)(14870,14995)(14871,14994)(14872,14993)(14873,14992)(14874,14991)(14875,14990)(14876,14989)(14877,14988)(14878,14987)(14879,14986)(14880,14985)(14881,14984)(14882,14983)(14883,14982)(14884,14981)(14885,14980)(14886,14979)(14887,14978)(14888,14977)(14889,14976)(14890,14975)(14891,14974)(14892,14973)(14893,14972)(14894,14971)(14895,14970)(14896,14969)(14897,14968)(14898,14967)(14899,14966)(14900,14965)(14901,14964)(14902,14963)(14903,14962)(14904,14961)(14905,14960)(14906,14959)(14907,14958)(14908,14957)(14909,14956)(14910,14955)(14911,14954)(14912,14953)(14913,14952)(14914,14951)(14915,14950)(14916,14949)(14917,14948)(14918,14947)(14919,14946)(14920,14945)(14921,14944)(14922,14943)(14923,14942)(14924,14941)(14925,14940)(14926,14939)(14927,14938)(14928,14937)(14929,14936)(14930,14935)(14931,14934)(14932,14933)

Polycyclic presentation:

2,29863|b^a=b^29862

Conjugacy classes & character table

14933 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(59726, 1);

D29863 #68713007