D₂₉₃₈₃ #67546973

order	58766
automorphism	Aut(G) order 863331306
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₉₃₈₃

Splittings

Fitting, socle, derived, Sylow

C₂₉₃₈₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉₃₈₃	C₂
LCS	G ▷ C₂₉₃₈₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29383
transitive degree	μ_t(G) = 29383

A minimal faithful permutation representation — 2 generators on 29383 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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5083)(14303,15082)(14304,15081)(14305,15080)(14306,15079)(14307,15078)(14308,15077)(14309,15076)(14310,15075)(14311,15074)(14312,15073)(14313,15072)(14314,15071)(14315,15070)(14316,15069)(14317,15068)(14318,15067)(14319,15066)(14320,15065)(14321,15064)(14322,15063)(14323,15062)(14324,15061)(14325,15060)(14326,15059)(14327,15058)(14328,15057)(14329,15056)(14330,15055)(14331,15054)(14332,15053)(14333,15052)(14334,15051)(14335,15050)(14336,15049)(14337,15048)(14338,15047)(14339,15046)(14340,15045)(14341,15044)(14342,15043)(14343,15042)(14344,15041)(14345,15040)(14346,15039)(14347,15038)(14348,15037)(14349,15036)(14350,15035)(14351,15034)(14352,15033)(14353,15032)(14354,15031)(14355,15030)(14356,15029)(14357,15028)(14358,15027)(14359,15026)(14360,15025)(14361,15024)(14362,15023)(14363,15022)(14364,15021)(14365,15020)(14366,15019)(14367,15018)(14368,15017)(14369,15016)(14370,15015)(14371,15014)(14372,15013)(14373,15012)(14374,15011)(14375,15010)(14376,15009)(14377,15008)(14378,15007)(14379,15006)(14380,15005)(14381,15004)(14382,15003)(14383,15002)(14384,15001)(14385,15000)(14386,14999)(14387,14998)(14388,14997)(14389,14996)(14390,14995)(14391,14994)(14392,14993)(14393,14992)(14394,14991)(14395,14990)(14396,14989)(14397,14988)(14398,14987)(14399,14986)(14400,14985)(14401,14984)(14402,14983)(14403,14982)(14404,14981)(14405,14980)(14406,14979)(14407,14978)(14408,14977)(14409,14976)(14410,14975)(14411,14974)(14412,14973)(14413,14972)(14414,14971)(14415,14970)(14416,14969)(14417,14968)(14418,14967)(14419,14966)(14420,14965)(14421,14964)(14422,14963)(14423,14962)(14424,14961)(14425,14960)(14426,14959)(14427,14958)(14428,14957)(14429,14956)(14430,14955)(14431,14954)(14432,14953)(14433,14952)(14434,14951)(14435,14950)(14436,14949)(14437,14948)(14438,14947)(14439,14946)(14440,14945)(14441,14944)(14442,14943)(14443,14942)(14444,14941)(14445,14940)(14446,14939)(14447,14938)(14448,14937)(14449,14936)(14450,14935)(14451,14934)(14452,14933)(14453,14932)(14454,14931)(14455,14930)(14456,14929)(14457,14928)(14458,14927)(14459,14926)(14460,14925)(14461,14924)(14462,14923)(14463,14922)(14464,14921)(14465,14920)(14466,14919)(14467,14918)(14468,14917)(14469,14916)(14470,14915)(14471,14914)(14472,14913)(14473,14912)(14474,14911)(14475,14910)(14476,14909)(14477,14908)(14478,14907)(14479,14906)(14480,14905)(14481,14904)(14482,14903)(14483,14902)(14484,14901)(14485,14900)(14486,14899)(14487,14898)(14488,14897)(14489,14896)(14490,14895)(14491,14894)(14492,14893)(14493,14892)(14494,14891)(14495,14890)(14496,14889)(14497,14888)(14498,14887)(14499,14886)(14500,14885)(14501,14884)(14502,14883)(14503,14882)(14504,14881)(14505,14880)(14506,14879)(14507,14878)(14508,14877)(14509,14876)(14510,14875)(14511,14874)(14512,14873)(14513,14872)(14514,14871)(14515,14870)(14516,14869)(14517,14868)(14518,14867)(14519,14866)(14520,14865)(14521,14864)(14522,14863)(14523,14862)(14524,14861)(14525,14860)(14526,14859)(14527,14858)(14528,14857)(14529,14856)(14530,14855)(14531,14854)(14532,14853)(14533,14852)(14534,14851)(14535,14850)(14536,14849)(14537,14848)(14538,14847)(14539,14846)(14540,14845)(14541,14844)(14542,14843)(14543,14842)(14544,14841)(14545,14840)(14546,14839)(14547,14838)(14548,14837)(14549,14836)(14550,14835)(14551,14834)(14552,14833)(14553,14832)(14554,14831)(14555,14830)(14556,14829)(14557,14828)(14558,14827)(14559,14826)(14560,14825)(14561,14824)(14562,14823)(14563,14822)(14564,14821)(14565,14820)(14566,14819)(14567,14818)(14568,14817)(14569,14816)(14570,14815)(14571,14814)(14572,14813)(14573,14812)(14574,14811)(14575,14810)(14576,14809)(14577,14808)(14578,14807)(14579,14806)(14580,14805)(14581,14804)(14582,14803)(14583,14802)(14584,14801)(14585,14800)(14586,14799)(14587,14798)(14588,14797)(14589,14796)(14590,14795)(14591,14794)(14592,14793)(14593,14792)(14594,14791)(14595,14790)(14596,14789)(14597,14788)(14598,14787)(14599,14786)(14600,14785)(14601,14784)(14602,14783)(14603,14782)(14604,14781)(14605,14780)(14606,14779)(14607,14778)(14608,14777)(14609,14776)(14610,14775)(14611,14774)(14612,14773)(14613,14772)(14614,14771)(14615,14770)(14616,14769)(14617,14768)(14618,14767)(14619,14766)(14620,14765)(14621,14764)(14622,14763)(14623,14762)(14624,14761)(14625,14760)(14626,14759)(14627,14758)(14628,14757)(14629,14756)(14630,14755)(14631,14754)(14632,14753)(14633,14752)(14634,14751)(14635,14750)(14636,14749)(14637,14748)(14638,14747)(14639,14746)(14640,14745)(14641,14744)(14642,14743)(14643,14742)(14644,14741)(14645,14740)(14646,14739)(14647,14738)(14648,14737)(14649,14736)(14650,14735)(14651,14734)(14652,14733)(14653,14732)(14654,14731)(14655,14730)(14656,14729)(14657,14728)(14658,14727)(14659,14726)(14660,14725)(14661,14724)(14662,14723)(14663,14722)(14664,14721)(14665,14720)(14666,14719)(14667,14718)(14668,14717)(14669,14716)(14670,14715)(14671,14714)(14672,14713)(14673,14712)(14674,14711)(14675,14710)(14676,14709)(14677,14708)(14678,14707)(14679,14706)(14680,14705)(14681,14704)(14682,14703)(14683,14702)(14684,14701)(14685,14700)(14686,14699)(14687,14698)(14688,14697)(14689,14696)(14690,14695)(14691,14694)(14692,14693)

Polycyclic presentation:

2,29383|b^a=b^29382

Conjugacy classes & character table

14693 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(58766, 1);

D29383 #67546973