D₂₈₅₅₉ #65290237

order	57118
automorphism	Aut(G) order 815587922
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₅₅₉

Splittings

Fitting, socle, derived, Sylow

C₂₈₅₅₉ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₈₅₅₉	C₂
LCS	G ▷ C₂₈₅₅₉
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28559
transitive degree	μ_t(G) = 28559

A minimal faithful permutation representation — 2 generators on 28559 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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648)(13914,14647)(13915,14646)(13916,14645)(13917,14644)(13918,14643)(13919,14642)(13920,14641)(13921,14640)(13922,14639)(13923,14638)(13924,14637)(13925,14636)(13926,14635)(13927,14634)(13928,14633)(13929,14632)(13930,14631)(13931,14630)(13932,14629)(13933,14628)(13934,14627)(13935,14626)(13936,14625)(13937,14624)(13938,14623)(13939,14622)(13940,14621)(13941,14620)(13942,14619)(13943,14618)(13944,14617)(13945,14616)(13946,14615)(13947,14614)(13948,14613)(13949,14612)(13950,14611)(13951,14610)(13952,14609)(13953,14608)(13954,14607)(13955,14606)(13956,14605)(13957,14604)(13958,14603)(13959,14602)(13960,14601)(13961,14600)(13962,14599)(13963,14598)(13964,14597)(13965,14596)(13966,14595)(13967,14594)(13968,14593)(13969,14592)(13970,14591)(13971,14590)(13972,14589)(13973,14588)(13974,14587)(13975,14586)(13976,14585)(13977,14584)(13978,14583)(13979,14582)(13980,14581)(13981,14580)(13982,14579)(13983,14578)(13984,14577)(13985,14576)(13986,14575)(13987,14574)(13988,14573)(13989,14572)(13990,14571)(13991,14570)(13992,14569)(13993,14568)(13994,14567)(13995,14566)(13996,14565)(13997,14564)(13998,14563)(13999,14562)(14000,14561)(14001,14560)(14002,14559)(14003,14558)(14004,14557)(14005,14556)(14006,14555)(14007,14554)(14008,14553)(14009,14552)(14010,14551)(14011,14550)(14012,14549)(14013,14548)(14014,14547)(14015,14546)(14016,14545)(14017,14544)(14018,14543)(14019,14542)(14020,14541)(14021,14540)(14022,14539)(14023,14538)(14024,14537)(14025,14536)(14026,14535)(14027,14534)(14028,14533)(14029,14532)(14030,14531)(14031,14530)(14032,14529)(14033,14528)(14034,14527)(14035,14526)(14036,14525)(14037,14524)(14038,14523)(14039,14522)(14040,14521)(14041,14520)(14042,14519)(14043,14518)(14044,14517)(14045,14516)(14046,14515)(14047,14514)(14048,14513)(14049,14512)(14050,14511)(14051,14510)(14052,14509)(14053,14508)(14054,14507)(14055,14506)(14056,14505)(14057,14504)(14058,14503)(14059,14502)(14060,14501)(14061,14500)(14062,14499)(14063,14498)(14064,14497)(14065,14496)(14066,14495)(14067,14494)(14068,14493)(14069,14492)(14070,14491)(14071,14490)(14072,14489)(14073,14488)(14074,14487)(14075,14486)(14076,14485)(14077,14484)(14078,14483)(14079,14482)(14080,14481)(14081,14480)(14082,14479)(14083,14478)(14084,14477)(14085,14476)(14086,14475)(14087,14474)(14088,14473)(14089,14472)(14090,14471)(14091,14470)(14092,14469)(14093,14468)(14094,14467)(14095,14466)(14096,14465)(14097,14464)(14098,14463)(14099,14462)(14100,14461)(14101,14460)(14102,14459)(14103,14458)(14104,14457)(14105,14456)(14106,14455)(14107,14454)(14108,14453)(14109,14452)(14110,14451)(14111,14450)(14112,14449)(14113,14448)(14114,14447)(14115,14446)(14116,14445)(14117,14444)(14118,14443)(14119,14442)(14120,14441)(14121,14440)(14122,14439)(14123,14438)(14124,14437)(14125,14436)(14126,14435)(14127,14434)(14128,14433)(14129,14432)(14130,14431)(14131,14430)(14132,14429)(14133,14428)(14134,14427)(14135,14426)(14136,14425)(14137,14424)(14138,14423)(14139,14422)(14140,14421)(14141,14420)(14142,14419)(14143,14418)(14144,14417)(14145,14416)(14146,14415)(14147,14414)(14148,14413)(14149,14412)(14150,14411)(14151,14410)(14152,14409)(14153,14408)(14154,14407)(14155,14406)(14156,14405)(14157,14404)(14158,14403)(14159,14402)(14160,14401)(14161,14400)(14162,14399)(14163,14398)(14164,14397)(14165,14396)(14166,14395)(14167,14394)(14168,14393)(14169,14392)(14170,14391)(14171,14390)(14172,14389)(14173,14388)(14174,14387)(14175,14386)(14176,14385)(14177,14384)(14178,14383)(14179,14382)(14180,14381)(14181,14380)(14182,14379)(14183,14378)(14184,14377)(14185,14376)(14186,14375)(14187,14374)(14188,14373)(14189,14372)(14190,14371)(14191,14370)(14192,14369)(14193,14368)(14194,14367)(14195,14366)(14196,14365)(14197,14364)(14198,14363)(14199,14362)(14200,14361)(14201,14360)(14202,14359)(14203,14358)(14204,14357)(14205,14356)(14206,14355)(14207,14354)(14208,14353)(14209,14352)(14210,14351)(14211,14350)(14212,14349)(14213,14348)(14214,14347)(14215,14346)(14216,14345)(14217,14344)(14218,14343)(14219,14342)(14220,14341)(14221,14340)(14222,14339)(14223,14338)(14224,14337)(14225,14336)(14226,14335)(14227,14334)(14228,14333)(14229,14332)(14230,14331)(14231,14330)(14232,14329)(14233,14328)(14234,14327)(14235,14326)(14236,14325)(14237,14324)(14238,14323)(14239,14322)(14240,14321)(14241,14320)(14242,14319)(14243,14318)(14244,14317)(14245,14316)(14246,14315)(14247,14314)(14248,14313)(14249,14312)(14250,14311)(14251,14310)(14252,14309)(14253,14308)(14254,14307)(14255,14306)(14256,14305)(14257,14304)(14258,14303)(14259,14302)(14260,14301)(14261,14300)(14262,14299)(14263,14298)(14264,14297)(14265,14296)(14266,14295)(14267,14294)(14268,14293)(14269,14292)(14270,14291)(14271,14290)(14272,14289)(14273,14288)(14274,14287)(14275,14286)(14276,14285)(14277,14284)(14278,14283)(14279,14282)(14280,14281)

Polycyclic presentation:

2,28559|b^a=b^28558

Conjugacy classes & character table

14281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(57118, 1);

D28559 #65290237