D₂₈₆₆₃ #65291259

order	57326
automorphism	Aut(G) order 821538906
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₆₆₃

Splittings

Fitting, socle, derived, Sylow

C₂₈₆₆₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₈₆₆₃	C₂
LCS	G ▷ C₂₈₆₆₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28663
transitive degree	μ_t(G) = 28663

A minimal faithful permutation representation — 2 generators on 28663 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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800)(13866,14799)(13867,14798)(13868,14797)(13869,14796)(13870,14795)(13871,14794)(13872,14793)(13873,14792)(13874,14791)(13875,14790)(13876,14789)(13877,14788)(13878,14787)(13879,14786)(13880,14785)(13881,14784)(13882,14783)(13883,14782)(13884,14781)(13885,14780)(13886,14779)(13887,14778)(13888,14777)(13889,14776)(13890,14775)(13891,14774)(13892,14773)(13893,14772)(13894,14771)(13895,14770)(13896,14769)(13897,14768)(13898,14767)(13899,14766)(13900,14765)(13901,14764)(13902,14763)(13903,14762)(13904,14761)(13905,14760)(13906,14759)(13907,14758)(13908,14757)(13909,14756)(13910,14755)(13911,14754)(13912,14753)(13913,14752)(13914,14751)(13915,14750)(13916,14749)(13917,14748)(13918,14747)(13919,14746)(13920,14745)(13921,14744)(13922,14743)(13923,14742)(13924,14741)(13925,14740)(13926,14739)(13927,14738)(13928,14737)(13929,14736)(13930,14735)(13931,14734)(13932,14733)(13933,14732)(13934,14731)(13935,14730)(13936,14729)(13937,14728)(13938,14727)(13939,14726)(13940,14725)(13941,14724)(13942,14723)(13943,14722)(13944,14721)(13945,14720)(13946,14719)(13947,14718)(13948,14717)(13949,14716)(13950,14715)(13951,14714)(13952,14713)(13953,14712)(13954,14711)(13955,14710)(13956,14709)(13957,14708)(13958,14707)(13959,14706)(13960,14705)(13961,14704)(13962,14703)(13963,14702)(13964,14701)(13965,14700)(13966,14699)(13967,14698)(13968,14697)(13969,14696)(13970,14695)(13971,14694)(13972,14693)(13973,14692)(13974,14691)(13975,14690)(13976,14689)(13977,14688)(13978,14687)(13979,14686)(13980,14685)(13981,14684)(13982,14683)(13983,14682)(13984,14681)(13985,14680)(13986,14679)(13987,14678)(13988,14677)(13989,14676)(13990,14675)(13991,14674)(13992,14673)(13993,14672)(13994,14671)(13995,14670)(13996,14669)(13997,14668)(13998,14667)(13999,14666)(14000,14665)(14001,14664)(14002,14663)(14003,14662)(14004,14661)(14005,14660)(14006,14659)(14007,14658)(14008,14657)(14009,14656)(14010,14655)(14011,14654)(14012,14653)(14013,14652)(14014,14651)(14015,14650)(14016,14649)(14017,14648)(14018,14647)(14019,14646)(14020,14645)(14021,14644)(14022,14643)(14023,14642)(14024,14641)(14025,14640)(14026,14639)(14027,14638)(14028,14637)(14029,14636)(14030,14635)(14031,14634)(14032,14633)(14033,14632)(14034,14631)(14035,14630)(14036,14629)(14037,14628)(14038,14627)(14039,14626)(14040,14625)(14041,14624)(14042,14623)(14043,14622)(14044,14621)(14045,14620)(14046,14619)(14047,14618)(14048,14617)(14049,14616)(14050,14615)(14051,14614)(14052,14613)(14053,14612)(14054,14611)(14055,14610)(14056,14609)(14057,14608)(14058,14607)(14059,14606)(14060,14605)(14061,14604)(14062,14603)(14063,14602)(14064,14601)(14065,14600)(14066,14599)(14067,14598)(14068,14597)(14069,14596)(14070,14595)(14071,14594)(14072,14593)(14073,14592)(14074,14591)(14075,14590)(14076,14589)(14077,14588)(14078,14587)(14079,14586)(14080,14585)(14081,14584)(14082,14583)(14083,14582)(14084,14581)(14085,14580)(14086,14579)(14087,14578)(14088,14577)(14089,14576)(14090,14575)(14091,14574)(14092,14573)(14093,14572)(14094,14571)(14095,14570)(14096,14569)(14097,14568)(14098,14567)(14099,14566)(14100,14565)(14101,14564)(14102,14563)(14103,14562)(14104,14561)(14105,14560)(14106,14559)(14107,14558)(14108,14557)(14109,14556)(14110,14555)(14111,14554)(14112,14553)(14113,14552)(14114,14551)(14115,14550)(14116,14549)(14117,14548)(14118,14547)(14119,14546)(14120,14545)(14121,14544)(14122,14543)(14123,14542)(14124,14541)(14125,14540)(14126,14539)(14127,14538)(14128,14537)(14129,14536)(14130,14535)(14131,14534)(14132,14533)(14133,14532)(14134,14531)(14135,14530)(14136,14529)(14137,14528)(14138,14527)(14139,14526)(14140,14525)(14141,14524)(14142,14523)(14143,14522)(14144,14521)(14145,14520)(14146,14519)(14147,14518)(14148,14517)(14149,14516)(14150,14515)(14151,14514)(14152,14513)(14153,14512)(14154,14511)(14155,14510)(14156,14509)(14157,14508)(14158,14507)(14159,14506)(14160,14505)(14161,14504)(14162,14503)(14163,14502)(14164,14501)(14165,14500)(14166,14499)(14167,14498)(14168,14497)(14169,14496)(14170,14495)(14171,14494)(14172,14493)(14173,14492)(14174,14491)(14175,14490)(14176,14489)(14177,14488)(14178,14487)(14179,14486)(14180,14485)(14181,14484)(14182,14483)(14183,14482)(14184,14481)(14185,14480)(14186,14479)(14187,14478)(14188,14477)(14189,14476)(14190,14475)(14191,14474)(14192,14473)(14193,14472)(14194,14471)(14195,14470)(14196,14469)(14197,14468)(14198,14467)(14199,14466)(14200,14465)(14201,14464)(14202,14463)(14203,14462)(14204,14461)(14205,14460)(14206,14459)(14207,14458)(14208,14457)(14209,14456)(14210,14455)(14211,14454)(14212,14453)(14213,14452)(14214,14451)(14215,14450)(14216,14449)(14217,14448)(14218,14447)(14219,14446)(14220,14445)(14221,14444)(14222,14443)(14223,14442)(14224,14441)(14225,14440)(14226,14439)(14227,14438)(14228,14437)(14229,14436)(14230,14435)(14231,14434)(14232,14433)(14233,14432)(14234,14431)(14235,14430)(14236,14429)(14237,14428)(14238,14427)(14239,14426)(14240,14425)(14241,14424)(14242,14423)(14243,14422)(14244,14421)(14245,14420)(14246,14419)(14247,14418)(14248,14417)(14249,14416)(142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Polycyclic presentation:

2,28663|b^a=b^28662

Conjugacy classes & character table

14333 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(57326, 1);

D28663 #65291259