D₂₈₆₈₇ #65291392

order	57374
automorphism	Aut(G) order 822915282
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₆₈₇

Splittings

Fitting, socle, derived, Sylow

C₂₈₆₈₇ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₈₆₈₇	C₂
LCS	G ▷ C₂₈₆₈₇
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28687
transitive degree	μ_t(G) = 28687

A minimal faithful permutation representation — 2 generators on 28687 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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4835)(13855,14834)(13856,14833)(13857,14832)(13858,14831)(13859,14830)(13860,14829)(13861,14828)(13862,14827)(13863,14826)(13864,14825)(13865,14824)(13866,14823)(13867,14822)(13868,14821)(13869,14820)(13870,14819)(13871,14818)(13872,14817)(13873,14816)(13874,14815)(13875,14814)(13876,14813)(13877,14812)(13878,14811)(13879,14810)(13880,14809)(13881,14808)(13882,14807)(13883,14806)(13884,14805)(13885,14804)(13886,14803)(13887,14802)(13888,14801)(13889,14800)(13890,14799)(13891,14798)(13892,14797)(13893,14796)(13894,14795)(13895,14794)(13896,14793)(13897,14792)(13898,14791)(13899,14790)(13900,14789)(13901,14788)(13902,14787)(13903,14786)(13904,14785)(13905,14784)(13906,14783)(13907,14782)(13908,14781)(13909,14780)(13910,14779)(13911,14778)(13912,14777)(13913,14776)(13914,14775)(13915,14774)(13916,14773)(13917,14772)(13918,14771)(13919,14770)(13920,14769)(13921,14768)(13922,14767)(13923,14766)(13924,14765)(13925,14764)(13926,14763)(13927,14762)(13928,14761)(13929,14760)(13930,14759)(13931,14758)(13932,14757)(13933,14756)(13934,14755)(13935,14754)(13936,14753)(13937,14752)(13938,14751)(13939,14750)(13940,14749)(13941,14748)(13942,14747)(13943,14746)(13944,14745)(13945,14744)(13946,14743)(13947,14742)(13948,14741)(13949,14740)(13950,14739)(13951,14738)(13952,14737)(13953,14736)(13954,14735)(13955,14734)(13956,14733)(13957,14732)(13958,14731)(13959,14730)(13960,14729)(13961,14728)(13962,14727)(13963,14726)(13964,14725)(13965,14724)(13966,14723)(13967,14722)(13968,14721)(13969,14720)(13970,14719)(13971,14718)(13972,14717)(13973,14716)(13974,14715)(13975,14714)(13976,14713)(13977,14712)(13978,14711)(13979,14710)(13980,14709)(13981,14708)(13982,14707)(13983,14706)(13984,14705)(13985,14704)(13986,14703)(13987,14702)(13988,14701)(13989,14700)(13990,14699)(13991,14698)(13992,14697)(13993,14696)(13994,14695)(13995,14694)(13996,14693)(13997,14692)(13998,14691)(13999,14690)(14000,14689)(14001,14688)(14002,14687)(14003,14686)(14004,14685)(14005,14684)(14006,14683)(14007,14682)(14008,14681)(14009,14680)(14010,14679)(14011,14678)(14012,14677)(14013,14676)(14014,14675)(14015,14674)(14016,14673)(14017,14672)(14018,14671)(14019,14670)(14020,14669)(14021,14668)(14022,14667)(14023,14666)(14024,14665)(14025,14664)(14026,14663)(14027,14662)(14028,14661)(14029,14660)(14030,14659)(14031,14658)(14032,14657)(14033,14656)(14034,14655)(14035,14654)(14036,14653)(14037,14652)(14038,14651)(14039,14650)(14040,14649)(14041,14648)(14042,14647)(14043,14646)(14044,14645)(14045,14644)(14046,14643)(14047,14642)(14048,14641)(14049,14640)(14050,14639)(14051,14638)(14052,14637)(14053,14636)(14054,14635)(14055,14634)(14056,14633)(14057,14632)(14058,14631)(14059,14630)(14060,14629)(14061,14628)(14062,14627)(14063,14626)(14064,14625)(14065,14624)(14066,14623)(14067,14622)(14068,14621)(14069,14620)(14070,14619)(14071,14618)(14072,14617)(14073,14616)(14074,14615)(14075,14614)(14076,14613)(14077,14612)(14078,14611)(14079,14610)(14080,14609)(14081,14608)(14082,14607)(14083,14606)(14084,14605)(14085,14604)(14086,14603)(14087,14602)(14088,14601)(14089,14600)(14090,14599)(14091,14598)(14092,14597)(14093,14596)(14094,14595)(14095,14594)(14096,14593)(14097,14592)(14098,14591)(14099,14590)(14100,14589)(14101,14588)(14102,14587)(14103,14586)(14104,14585)(14105,14584)(14106,14583)(14107,14582)(14108,14581)(14109,14580)(14110,14579)(14111,14578)(14112,14577)(14113,14576)(14114,14575)(14115,14574)(14116,14573)(14117,14572)(14118,14571)(14119,14570)(14120,14569)(14121,14568)(14122,14567)(14123,14566)(14124,14565)(14125,14564)(14126,14563)(14127,14562)(14128,14561)(14129,14560)(14130,14559)(14131,14558)(14132,14557)(14133,14556)(14134,14555)(14135,14554)(14136,14553)(14137,14552)(14138,14551)(14139,14550)(14140,14549)(14141,14548)(14142,14547)(14143,14546)(14144,14545)(14145,14544)(14146,14543)(14147,14542)(14148,14541)(14149,14540)(14150,14539)(14151,14538)(14152,14537)(14153,14536)(14154,14535)(14155,14534)(14156,14533)(14157,14532)(14158,14531)(14159,14530)(14160,14529)(14161,14528)(14162,14527)(14163,14526)(14164,14525)(14165,14524)(14166,14523)(14167,14522)(14168,14521)(14169,14520)(14170,14519)(14171,14518)(14172,14517)(14173,14516)(14174,14515)(14175,14514)(14176,14513)(14177,14512)(14178,14511)(14179,14510)(14180,14509)(14181,14508)(14182,14507)(14183,14506)(14184,14505)(14185,14504)(14186,14503)(14187,14502)(14188,14501)(14189,14500)(14190,14499)(14191,14498)(14192,14497)(14193,14496)(14194,14495)(14195,14494)(14196,14493)(14197,14492)(14198,14491)(14199,14490)(14200,14489)(14201,14488)(14202,14487)(14203,14486)(14204,14485)(14205,14484)(14206,14483)(14207,14482)(14208,14481)(14209,14480)(14210,14479)(14211,14478)(14212,14477)(14213,14476)(14214,14475)(14215,14474)(14216,14473)(14217,14472)(14218,14471)(14219,14470)(14220,14469)(14221,14468)(14222,14467)(14223,14466)(14224,14465)(14225,14464)(14226,14463)(14227,14462)(14228,14461)(14229,14460)(14230,14459)(14231,14458)(14232,14457)(14233,14456)(14234,14455)(14235,14454)(14236,14453)(14237,14452)(14238,14451)(14239,14450)(14240,14449)(14241,14448)(14242,14447)(14243,14446)(14244,14445)(14245,14444)(14246,14443)(14247,14442)(14248,14441)(14249,14440)(14250,14439)(14251,14438)(14252,14437)(14253,14436)(14254,14435)(14255,14434)(14256,14433)(14257,14432)(14258,14431)(14259,14430)(14260,14429)(14261,14428)(14262,14427)(14263,14426)(14264,14425)(14265,14424)(14266,14423)(14267,14422)(14268,14421)(14269,14420)(14270,14419)(14271,14418)(14272,14417)(14273,14416)(14274,14415)(14275,14414)(14276,14413)(14277,14412)(14278,14411)(14279,14410)(14280,14409)(14281,14408)(14282,14407)(14283,14406)(14284,14405)(14285,14404)(14286,14403)(14287,14402)(14288,14401)(14289,14400)(14290,14399)(14291,14398)(14292,14397)(14293,14396)(14294,14395)(14295,14394)(14296,14393)(14297,14392)(14298,14391)(14299,14390)(14300,14389)(14301,14388)(14302,14387)(14303,14386)(14304,14385)(14305,14384)(14306,14383)(14307,14382)(14308,14381)(14309,14380)(14310,14379)(14311,14378)(14312,14377)(14313,14376)(14314,14375)(14315,14374)(14316,14373)(14317,14372)(14318,14371)(14319,14370)(14320,14369)(14321,14368)(14322,14367)(14323,14366)(14324,14365)(14325,14364)(14326,14363)(14327,14362)(14328,14361)(14329,14360)(14330,14359)(14331,14358)(14332,14357)(14333,14356)(14334,14355)(14335,14354)(14336,14353)(14337,14352)(14338,14351)(14339,14350)(14340,14349)(14341,14348)(14342,14347)(14343,14346)(14344,14345)

Polycyclic presentation:

2,28687|b^a=b^28686

Conjugacy classes & character table

14345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(57374, 1);

D28687 #65291392