D₂₈₃₉₃ #64205339

order	56786
automorphism	Aut(G) order 806134056
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₃₉₃

Splittings

Fitting, socle, derived, Sylow

C₂₈₃₉₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₈₃₉₃	C₂
LCS	G ▷ C₂₈₃₉₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28393
transitive degree	μ_t(G) = 28393

A minimal faithful permutation representation — 2 generators on 28393 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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790)(13606,14789)(13607,14788)(13608,14787)(13609,14786)(13610,14785)(13611,14784)(13612,14783)(13613,14782)(13614,14781)(13615,14780)(13616,14779)(13617,14778)(13618,14777)(13619,14776)(13620,14775)(13621,14774)(13622,14773)(13623,14772)(13624,14771)(13625,14770)(13626,14769)(13627,14768)(13628,14767)(13629,14766)(13630,14765)(13631,14764)(13632,14763)(13633,14762)(13634,14761)(13635,14760)(13636,14759)(13637,14758)(13638,14757)(13639,14756)(13640,14755)(13641,14754)(13642,14753)(13643,14752)(13644,14751)(13645,14750)(13646,14749)(13647,14748)(13648,14747)(13649,14746)(13650,14745)(13651,14744)(13652,14743)(13653,14742)(13654,14741)(13655,14740)(13656,14739)(13657,14738)(13658,14737)(13659,14736)(13660,14735)(13661,14734)(13662,14733)(13663,14732)(13664,14731)(13665,14730)(13666,14729)(13667,14728)(13668,14727)(13669,14726)(13670,14725)(13671,14724)(13672,14723)(13673,14722)(13674,14721)(13675,14720)(13676,14719)(13677,14718)(13678,14717)(13679,14716)(13680,14715)(13681,14714)(13682,14713)(13683,14712)(13684,14711)(13685,14710)(13686,14709)(13687,14708)(13688,14707)(13689,14706)(13690,14705)(13691,14704)(13692,14703)(13693,14702)(13694,14701)(13695,14700)(13696,14699)(13697,14698)(13698,14697)(13699,14696)(13700,14695)(13701,14694)(13702,14693)(13703,14692)(13704,14691)(13705,14690)(13706,14689)(13707,14688)(13708,14687)(13709,14686)(13710,14685)(13711,14684)(13712,14683)(13713,14682)(13714,14681)(13715,14680)(13716,14679)(13717,14678)(13718,14677)(13719,14676)(13720,14675)(13721,14674)(13722,14673)(13723,14672)(13724,14671)(13725,14670)(13726,14669)(13727,14668)(13728,14667)(13729,14666)(13730,14665)(13731,14664)(13732,14663)(13733,14662)(13734,14661)(13735,14660)(13736,14659)(13737,14658)(13738,14657)(13739,14656)(13740,14655)(13741,14654)(13742,14653)(13743,14652)(13744,14651)(13745,14650)(13746,14649)(13747,14648)(13748,14647)(13749,14646)(13750,14645)(13751,14644)(13752,14643)(13753,14642)(13754,14641)(13755,14640)(13756,14639)(13757,14638)(13758,14637)(13759,14636)(13760,14635)(13761,14634)(13762,14633)(13763,14632)(13764,14631)(13765,14630)(13766,14629)(13767,14628)(13768,14627)(13769,14626)(13770,14625)(13771,14624)(13772,14623)(13773,14622)(13774,14621)(13775,14620)(13776,14619)(13777,14618)(13778,14617)(13779,14616)(13780,14615)(13781,14614)(13782,14613)(13783,14612)(13784,14611)(13785,14610)(13786,14609)(13787,14608)(13788,14607)(13789,14606)(13790,14605)(13791,14604)(13792,14603)(13793,14602)(13794,14601)(13795,14600)(13796,14599)(13797,14598)(13798,14597)(13799,14596)(13800,14595)(13801,14594)(13802,14593)(13803,14592)(13804,14591)(13805,14590)(13806,14589)(13807,14588)(13808,14587)(13809,14586)(13810,14585)(13811,14584)(13812,14583)(13813,14582)(13814,14581)(13815,14580)(13816,14579)(13817,14578)(13818,14577)(13819,14576)(13820,14575)(13821,14574)(13822,14573)(13823,14572)(13824,14571)(13825,14570)(13826,14569)(13827,14568)(13828,14567)(13829,14566)(13830,14565)(13831,14564)(13832,14563)(13833,14562)(13834,14561)(13835,14560)(13836,14559)(13837,14558)(13838,14557)(13839,14556)(13840,14555)(13841,14554)(13842,14553)(13843,14552)(13844,14551)(13845,14550)(13846,14549)(13847,14548)(13848,14547)(13849,14546)(13850,14545)(13851,14544)(13852,14543)(13853,14542)(13854,14541)(13855,14540)(13856,14539)(13857,14538)(13858,14537)(13859,14536)(13860,14535)(13861,14534)(13862,14533)(13863,14532)(13864,14531)(13865,14530)(13866,14529)(13867,14528)(13868,14527)(13869,14526)(13870,14525)(13871,14524)(13872,14523)(13873,14522)(13874,14521)(13875,14520)(13876,14519)(13877,14518)(13878,14517)(13879,14516)(13880,14515)(13881,14514)(13882,14513)(13883,14512)(13884,14511)(13885,14510)(13886,14509)(13887,14508)(13888,14507)(13889,14506)(13890,14505)(13891,14504)(13892,14503)(13893,14502)(13894,14501)(13895,14500)(13896,14499)(13897,14498)(13898,14497)(13899,14496)(13900,14495)(13901,14494)(13902,14493)(13903,14492)(13904,14491)(13905,14490)(13906,14489)(13907,14488)(13908,14487)(13909,14486)(13910,14485)(13911,14484)(13912,14483)(13913,14482)(13914,14481)(13915,14480)(13916,14479)(13917,14478)(13918,14477)(13919,14476)(13920,14475)(13921,14474)(13922,14473)(13923,14472)(13924,14471)(13925,14470)(13926,14469)(13927,14468)(13928,14467)(13929,14466)(13930,14465)(13931,14464)(13932,14463)(13933,14462)(13934,14461)(13935,14460)(13936,14459)(13937,14458)(13938,14457)(13939,14456)(13940,14455)(13941,14454)(13942,14453)(13943,14452)(13944,14451)(13945,14450)(13946,14449)(13947,14448)(13948,14447)(13949,14446)(13950,14445)(13951,14444)(13952,14443)(13953,14442)(13954,14441)(13955,14440)(13956,14439)(13957,14438)(13958,14437)(13959,14436)(13960,14435)(13961,14434)(13962,14433)(13963,14432)(13964,14431)(13965,14430)(13966,14429)(13967,14428)(13968,14427)(13969,14426)(13970,14425)(13971,14424)(13972,14423)(13973,14422)(13974,14421)(13975,14420)(13976,14419)(13977,14418)(13978,14417)(13979,14416)(13980,14415)(13981,14414)(13982,14413)(13983,14412)(13984,14411)(13985,14410)(13986,14409)(13987,14408)(13988,14407)(13989,14406)(13990,14405)(13991,14404)(13992,14403)(13993,14402)(13994,14401)(13995,14400)(13996,14399)(13997,14398)(13998,14397)(13999,14396)(14000,14395)(14001,14394)(14002,14393)(14003,14392)(14004,14391)(14005,14390)(14006,14389)(14007,14388)(14008,14387)(14009,14386)(14010,14385)(14011,14384)(14012,14383)(14013,14382)(14014,14381)(14015,14380)(14016,14379)(14017,14378)(14018,14377)(14019,14376)(14020,14375)(14021,14374)(14022,14373)(14023,14372)(14024,14371)(14025,14370)(14026,14369)(14027,14368)(14028,14367)(14029,14366)(14030,14365)(14031,14364)(14032,14363)(14033,14362)(14034,14361)(14035,14360)(14036,14359)(14037,14358)(14038,14357)(14039,14356)(14040,14355)(14041,14354)(14042,14353)(14043,14352)(14044,14351)(14045,14350)(14046,14349)(14047,14348)(14048,14347)(14049,14346)(14050,14345)(14051,14344)(14052,14343)(14053,14342)(14054,14341)(14055,14340)(14056,14339)(14057,14338)(14058,14337)(14059,14336)(14060,14335)(14061,14334)(14062,14333)(14063,14332)(14064,14331)(14065,14330)(14066,14329)(14067,14328)(14068,14327)(14069,14326)(14070,14325)(14071,14324)(14072,14323)(14073,14322)(14074,14321)(14075,14320)(14076,14319)(14077,14318)(14078,14317)(14079,14316)(14080,14315)(14081,14314)(14082,14313)(14083,14312)(14084,14311)(14085,14310)(14086,14309)(14087,14308)(14088,14307)(14089,14306)(14090,14305)(14091,14304)(14092,14303)(14093,14302)(14094,14301)(14095,14300)(14096,14299)(14097,14298)(14098,14297)(14099,14296)(14100,14295)(14101,14294)(14102,14293)(14103,14292)(14104,14291)(14105,14290)(14106,14289)(14107,14288)(14108,14287)(14109,14286)(14110,14285)(14111,14284)(14112,14283)(14113,14282)(14114,14281)(14115,14280)(14116,14279)(14117,14278)(14118,14277)(14119,14276)(14120,14275)(14121,14274)(14122,14273)(14123,14272)(14124,14271)(14125,14270)(14126,14269)(14127,14268)(14128,14267)(14129,14266)(14130,14265)(14131,14264)(14132,14263)(14133,14262)(14134,14261)(14135,14260)(14136,14259)(14137,14258)(14138,14257)(14139,14256)(14140,14255)(14141,14254)(14142,14253)(14143,14252)(14144,14251)(14145,14250)(14146,14249)(14147,14248)(14148,14247)(14149,14246)(14150,14245)(14151,14244)(14152,14243)(14153,14242)(14154,14241)(14155,14240)(14156,14239)(14157,14238)(14158,14237)(14159,14236)(14160,14235)(14161,14234)(14162,14233)(14163,14232)(14164,14231)(14165,14230)(14166,14229)(14167,14228)(14168,14227)(14169,14226)(14170,14225)(14171,14224)(14172,14223)(14173,14222)(14174,14221)(14175,14220)(14176,14219)(14177,14218)(14178,14217)(14179,14216)(14180,14215)(14181,14214)(14182,14213)(14183,14212)(14184,14211)(14185,14210)(14186,14209)(14187,14208)(14188,14207)(14189,14206)(14190,14205)(14191,14204)(14192,14203)(14193,14202)(14194,14201)(14195,14200)(14196,14199)(14197,14198)

Polycyclic presentation:

2,28393|b^a=b^28392

Conjugacy classes & character table

14198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(56786, 1);

D28393 #64205339