D₂₈₇₈₉ #65313868

order	57578
automorphism	Aut(G) order 828777732
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₇₈₉

Splittings

Fitting, socle, derived, Sylow

C₂₈₇₈₉ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₈₇₈₉	C₂
LCS	G ▷ C₂₈₇₈₉
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28789
transitive degree	μ_t(G) = 28789

A minimal faithful permutation representation — 2 generators on 28789 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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14984)(13808,14983)(13809,14982)(13810,14981)(13811,14980)(13812,14979)(13813,14978)(13814,14977)(13815,14976)(13816,14975)(13817,14974)(13818,14973)(13819,14972)(13820,14971)(13821,14970)(13822,14969)(13823,14968)(13824,14967)(13825,14966)(13826,14965)(13827,14964)(13828,14963)(13829,14962)(13830,14961)(13831,14960)(13832,14959)(13833,14958)(13834,14957)(13835,14956)(13836,14955)(13837,14954)(13838,14953)(13839,14952)(13840,14951)(13841,14950)(13842,14949)(13843,14948)(13844,14947)(13845,14946)(13846,14945)(13847,14944)(13848,14943)(13849,14942)(13850,14941)(13851,14940)(13852,14939)(13853,14938)(13854,14937)(13855,14936)(13856,14935)(13857,14934)(13858,14933)(13859,14932)(13860,14931)(13861,14930)(13862,14929)(13863,14928)(13864,14927)(13865,14926)(13866,14925)(13867,14924)(13868,14923)(13869,14922)(13870,14921)(13871,14920)(13872,14919)(13873,14918)(13874,14917)(13875,14916)(13876,14915)(13877,14914)(13878,14913)(13879,14912)(13880,14911)(13881,14910)(13882,14909)(13883,14908)(13884,14907)(13885,14906)(13886,14905)(13887,14904)(13888,14903)(13889,14902)(13890,14901)(13891,14900)(13892,14899)(13893,14898)(13894,14897)(13895,14896)(13896,14895)(13897,14894)(13898,14893)(13899,14892)(13900,14891)(13901,14890)(13902,14889)(13903,14888)(13904,14887)(13905,14886)(13906,14885)(13907,14884)(13908,14883)(13909,14882)(13910,14881)(13911,14880)(13912,14879)(13913,14878)(13914,14877)(13915,14876)(13916,14875)(13917,14874)(13918,14873)(13919,14872)(13920,14871)(13921,14870)(13922,14869)(13923,14868)(13924,14867)(13925,14866)(13926,14865)(13927,14864)(13928,14863)(13929,14862)(13930,14861)(13931,14860)(13932,14859)(13933,14858)(13934,14857)(13935,14856)(13936,14855)(13937,14854)(13938,14853)(13939,14852)(13940,14851)(13941,14850)(13942,14849)(13943,14848)(13944,14847)(13945,14846)(13946,14845)(13947,14844)(13948,14843)(13949,14842)(13950,14841)(13951,14840)(13952,14839)(13953,14838)(13954,14837)(13955,14836)(13956,14835)(13957,14834)(13958,14833)(13959,14832)(13960,14831)(13961,14830)(13962,14829)(13963,14828)(13964,14827)(13965,14826)(13966,14825)(13967,14824)(13968,14823)(13969,14822)(13970,14821)(13971,14820)(13972,14819)(13973,14818)(13974,14817)(13975,14816)(13976,14815)(13977,14814)(13978,14813)(13979,14812)(13980,14811)(13981,14810)(13982,14809)(13983,14808)(13984,14807)(13985,14806)(13986,14805)(13987,14804)(13988,14803)(13989,14802)(13990,14801)(13991,14800)(13992,14799)(13993,14798)(13994,14797)(13995,14796)(13996,14795)(13997,14794)(13998,14793)(13999,14792)(14000,14791)(14001,14790)(14002,14789)(14003,14788)(14004,14787)(14005,14786)(14006,14785)(14007,14784)(14008,14783)(14009,14782)(14010,14781)(14011,14780)(14012,14779)(14013,14778)(14014,14777)(14015,14776)(14016,14775)(14017,14774)(14018,14773)(14019,14772)(14020,14771)(14021,14770)(14022,14769)(14023,14768)(14024,14767)(14025,14766)(14026,14765)(14027,14764)(14028,14763)(14029,14762)(14030,14761)(14031,14760)(14032,14759)(14033,14758)(14034,14757)(14035,14756)(14036,14755)(14037,14754)(14038,14753)(14039,14752)(14040,14751)(14041,14750)(14042,14749)(14043,14748)(14044,14747)(14045,14746)(14046,14745)(14047,14744)(14048,14743)(14049,14742)(14050,14741)(14051,14740)(14052,14739)(14053,14738)(14054,14737)(14055,14736)(14056,14735)(14057,14734)(14058,14733)(14059,14732)(14060,14731)(14061,14730)(14062,14729)(14063,14728)(14064,14727)(14065,14726)(14066,14725)(14067,14724)(14068,14723)(14069,14722)(14070,14721)(14071,14720)(14072,14719)(14073,14718)(14074,14717)(14075,14716)(14076,14715)(14077,14714)(14078,14713)(14079,14712)(14080,14711)(14081,14710)(14082,14709)(14083,14708)(14084,14707)(14085,14706)(14086,14705)(14087,14704)(14088,14703)(14089,14702)(14090,14701)(14091,14700)(14092,14699)(14093,14698)(14094,14697)(14095,14696)(14096,14695)(14097,14694)(14098,14693)(14099,14692)(14100,14691)(14101,14690)(14102,14689)(14103,14688)(14104,14687)(14105,14686)(14106,14685)(14107,14684)(14108,14683)(14109,14682)(14110,14681)(14111,14680)(14112,14679)(14113,14678)(14114,14677)(14115,14676)(14116,14675)(14117,14674)(14118,14673)(14119,14672)(14120,14671)(14121,14670)(14122,14669)(14123,14668)(14124,14667)(14125,14666)(14126,14665)(14127,14664)(14128,14663)(14129,14662)(14130,14661)(14131,14660)(14132,14659)(14133,14658)(14134,14657)(14135,14656)(14136,14655)(14137,14654)(14138,14653)(14139,14652)(14140,14651)(14141,14650)(14142,14649)(14143,14648)(14144,14647)(14145,14646)(14146,14645)(14147,14644)(14148,14643)(14149,14642)(14150,14641)(14151,14640)(14152,14639)(14153,14638)(14154,14637)(14155,14636)(14156,14635)(14157,14634)(14158,14633)(14159,14632)(14160,14631)(14161,14630)(14162,14629)(14163,14628)(14164,14627)(14165,14626)(14166,14625)(14167,14624)(14168,14623)(14169,14622)(14170,14621)(14171,14620)(14172,14619)(14173,14618)(14174,14617)(14175,14616)(14176,14615)(14177,14614)(14178,14613)(14179,14612)(14180,14611)(14181,14610)(14182,14609)(14183,14608)(14184,14607)(14185,14606)(14186,14605)(14187,14604)(14188,14603)(14189,14602)(14190,14601)(14191,14600)(14192,14599)(14193,14598)(14194,14597)(14195,14596)(14196,14595)(14197,14594)(14198,14593)(14199,14592)(14200,14591)(14201,14590)(14202,14589)(14203,14588)(14204,14587)(14205,14586)(14206,14585)(14207,14584)(14208,14583)(14209,14582)(14210,14581)(14211,14580)(14212,14579)(14213,14578)(14214,14577)(14215,14576)(14216,14575)(14217,14574)(14218,14573)(14219,14572)(14220,14571)(14221,14570)(14222,14569)(14223,14568)(14224,14567)(14225,14566)(14226,14565)(14227,14564)(14228,14563)(14229,14562)(14230,14561)(14231,14560)(14232,14559)(14233,14558)(14234,14557)(14235,14556)(14236,14555)(14237,14554)(14238,14553)(14239,14552)(14240,14551)(14241,14550)(14242,14549)(14243,14548)(14244,14547)(14245,14546)(14246,14545)(14247,14544)(14248,14543)(14249,14542)(14250,14541)(14251,14540)(14252,14539)(14253,14538)(14254,14537)(14255,14536)(14256,14535)(14257,14534)(14258,14533)(14259,14532)(14260,14531)(14261,14530)(14262,14529)(14263,14528)(14264,14527)(14265,14526)(14266,14525)(14267,14524)(14268,14523)(14269,14522)(14270,14521)(14271,14520)(14272,14519)(14273,14518)(14274,14517)(14275,14516)(14276,14515)(14277,14514)(14278,14513)(14279,14512)(14280,14511)(14281,14510)(14282,14509)(14283,14508)(14284,14507)(14285,14506)(14286,14505)(14287,14504)(14288,14503)(14289,14502)(14290,14501)(14291,14500)(14292,14499)(14293,14498)(14294,14497)(14295,14496)(14296,14495)(14297,14494)(14298,14493)(14299,14492)(14300,14491)(14301,14490)(14302,14489)(14303,14488)(14304,14487)(14305,14486)(14306,14485)(14307,14484)(14308,14483)(14309,14482)(14310,14481)(14311,14480)(14312,14479)(14313,14478)(14314,14477)(14315,14476)(14316,14475)(14317,14474)(14318,14473)(14319,14472)(14320,14471)(14321,14470)(14322,14469)(14323,14468)(14324,14467)(14325,14466)(14326,14465)(14327,14464)(14328,14463)(14329,14462)(14330,14461)(14331,14460)(14332,14459)(14333,14458)(14334,14457)(14335,14456)(14336,14455)(14337,14454)(14338,14453)(14339,14452)(14340,14451)(14341,14450)(14342,14449)(14343,14448)(14344,14447)(14345,14446)(14346,14445)(14347,14444)(14348,14443)(14349,14442)(14350,14441)(14351,14440)(14352,14439)(14353,14438)(14354,14437)(14355,14436)(14356,14435)(14357,14434)(14358,14433)(14359,14432)(14360,14431)(14361,14430)(14362,14429)(14363,14428)(14364,14427)(14365,14426)(14366,14425)(14367,14424)(14368,14423)(14369,14422)(14370,14421)(14371,14420)(14372,14419)(14373,14418)(14374,14417)(14375,14416)(14376,14415)(14377,14414)(14378,14413)(14379,14412)(14380,14411)(14381,14410)(14382,14409)(14383,14408)(14384,14407)(14385,14406)(14386,14405)(14387,14404)(14388,14403)(14389,14402)(14390,14401)(14391,14400)(14392,14399)(14393,14398)(14394,14397)(14395,14396)

Polycyclic presentation:

2,28789|b^a=b^28788

Conjugacy classes & character table

14396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(57578, 1);

D28789 #65313868