D₂₈₇₅₁ #65313656

order	57502
automorphism	Aut(G) order 826591250
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₇₅₁

Splittings

Fitting, socle, derived, Sylow

C₂₈₇₅₁ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₈₇₅₁	C₂
LCS	G ▷ C₂₈₇₅₁
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28751
transitive degree	μ_t(G) = 28751

A minimal faithful permutation representation — 2 generators on 28751 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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544)(14210,14543)(14211,14542)(14212,14541)(14213,14540)(14214,14539)(14215,14538)(14216,14537)(14217,14536)(14218,14535)(14219,14534)(14220,14533)(14221,14532)(14222,14531)(14223,14530)(14224,14529)(14225,14528)(14226,14527)(14227,14526)(14228,14525)(14229,14524)(14230,14523)(14231,14522)(14232,14521)(14233,14520)(14234,14519)(14235,14518)(14236,14517)(14237,14516)(14238,14515)(14239,14514)(14240,14513)(14241,14512)(14242,14511)(14243,14510)(14244,14509)(14245,14508)(14246,14507)(14247,14506)(14248,14505)(14249,14504)(14250,14503)(14251,14502)(14252,14501)(14253,14500)(14254,14499)(14255,14498)(14256,14497)(14257,14496)(14258,14495)(14259,14494)(14260,14493)(14261,14492)(14262,14491)(14263,14490)(14264,14489)(14265,14488)(14266,14487)(14267,14486)(14268,14485)(14269,14484)(14270,14483)(14271,14482)(14272,14481)(14273,14480)(14274,14479)(14275,14478)(14276,14477)(14277,14476)(14278,14475)(14279,14474)(14280,14473)(14281,14472)(14282,14471)(14283,14470)(14284,14469)(14285,14468)(14286,14467)(14287,14466)(14288,14465)(14289,14464)(14290,14463)(14291,14462)(14292,14461)(14293,14460)(14294,14459)(14295,14458)(14296,14457)(14297,14456)(14298,14455)(14299,14454)(14300,14453)(14301,14452)(14302,14451)(14303,14450)(14304,14449)(14305,14448)(14306,14447)(14307,14446)(14308,14445)(14309,14444)(14310,14443)(14311,14442)(14312,14441)(14313,14440)(14314,14439)(14315,14438)(14316,14437)(14317,14436)(14318,14435)(14319,14434)(14320,14433)(14321,14432)(14322,14431)(14323,14430)(14324,14429)(14325,14428)(14326,14427)(14327,14426)(14328,14425)(14329,14424)(14330,14423)(14331,14422)(14332,14421)(14333,14420)(14334,14419)(14335,14418)(14336,14417)(14337,14416)(14338,14415)(14339,14414)(14340,14413)(14341,14412)(14342,14411)(14343,14410)(14344,14409)(14345,14408)(14346,14407)(14347,14406)(14348,14405)(14349,14404)(14350,14403)(14351,14402)(14352,14401)(14353,14400)(14354,14399)(14355,14398)(14356,14397)(14357,14396)(14358,14395)(14359,14394)(14360,14393)(14361,14392)(14362,14391)(14363,14390)(14364,14389)(14365,14388)(14366,14387)(14367,14386)(14368,14385)(14369,14384)(14370,14383)(14371,14382)(14372,14381)(14373,14380)(14374,14379)(14375,14378)(14376,14377)

Polycyclic presentation:

2,28751|b^a=b^28750

Conjugacy classes & character table

14377 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(57502, 1);

D28751 #65313656