D₃₁₆₂₇ #71019308

order	63254
automorphism	Aut(G) order 1000235502
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₃₁₆₂₇

Splittings

Fitting, socle, derived, Sylow

C₃₁₆₂₇ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁₆₂₇	C₂
LCS	G ▷ C₃₁₆₂₇
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31627
transitive degree	μ_t(G) = 31627

A minimal faithful permutation representation — 2 generators on 31627 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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6055)(15575,16054)(15576,16053)(15577,16052)(15578,16051)(15579,16050)(15580,16049)(15581,16048)(15582,16047)(15583,16046)(15584,16045)(15585,16044)(15586,16043)(15587,16042)(15588,16041)(15589,16040)(15590,16039)(15591,16038)(15592,16037)(15593,16036)(15594,16035)(15595,16034)(15596,16033)(15597,16032)(15598,16031)(15599,16030)(15600,16029)(15601,16028)(15602,16027)(15603,16026)(15604,16025)(15605,16024)(15606,16023)(15607,16022)(15608,16021)(15609,16020)(15610,16019)(15611,16018)(15612,16017)(15613,16016)(15614,16015)(15615,16014)(15616,16013)(15617,16012)(15618,16011)(15619,16010)(15620,16009)(15621,16008)(15622,16007)(15623,16006)(15624,16005)(15625,16004)(15626,16003)(15627,16002)(15628,16001)(15629,16000)(15630,15999)(15631,15998)(15632,15997)(15633,15996)(15634,15995)(15635,15994)(15636,15993)(15637,15992)(15638,15991)(15639,15990)(15640,15989)(15641,15988)(15642,15987)(15643,15986)(15644,15985)(15645,15984)(15646,15983)(15647,15982)(15648,15981)(15649,15980)(15650,15979)(15651,15978)(15652,15977)(15653,15976)(15654,15975)(15655,15974)(15656,15973)(15657,15972)(15658,15971)(15659,15970)(15660,15969)(15661,15968)(15662,15967)(15663,15966)(15664,15965)(15665,15964)(15666,15963)(15667,15962)(15668,15961)(15669,15960)(15670,15959)(15671,15958)(15672,15957)(15673,15956)(15674,15955)(15675,15954)(15676,15953)(15677,15952)(15678,15951)(15679,15950)(15680,15949)(15681,15948)(15682,15947)(15683,15946)(15684,15945)(15685,15944)(15686,15943)(15687,15942)(15688,15941)(15689,15940)(15690,15939)(15691,15938)(15692,15937)(15693,15936)(15694,15935)(15695,15934)(15696,15933)(15697,15932)(15698,15931)(15699,15930)(15700,15929)(15701,15928)(15702,15927)(15703,15926)(15704,15925)(15705,15924)(15706,15923)(15707,15922)(15708,15921)(15709,15920)(15710,15919)(15711,15918)(15712,15917)(15713,15916)(15714,15915)(15715,15914)(15716,15913)(15717,15912)(15718,15911)(15719,15910)(15720,15909)(15721,15908)(15722,15907)(15723,15906)(15724,15905)(15725,15904)(15726,15903)(15727,15902)(15728,15901)(15729,15900)(15730,15899)(15731,15898)(15732,15897)(15733,15896)(15734,15895)(15735,15894)(15736,15893)(15737,15892)(15738,15891)(15739,15890)(15740,15889)(15741,15888)(15742,15887)(15743,15886)(15744,15885)(15745,15884)(15746,15883)(15747,15882)(15748,15881)(15749,15880)(15750,15879)(15751,15878)(15752,15877)(15753,15876)(15754,15875)(15755,15874)(15756,15873)(15757,15872)(15758,15871)(15759,15870)(15760,15869)(15761,15868)(15762,15867)(15763,15866)(15764,15865)(15765,15864)(15766,15863)(15767,15862)(15768,15861)(15769,15860)(15770,15859)(15771,15858)(15772,15857)(15773,15856)(15774,15855)(15775,15854)(15776,15853)(15777,15852)(15778,15851)(15779,15850)(15780,15849)(15781,15848)(15782,15847)(15783,15846)(15784,15845)(15785,15844)(15786,15843)(15787,15842)(15788,15841)(15789,15840)(15790,15839)(15791,15838)(15792,15837)(15793,15836)(15794,15835)(15795,15834)(15796,15833)(15797,15832)(15798,15831)(15799,15830)(15800,15829)(15801,15828)(15802,15827)(15803,15826)(15804,15825)(15805,15824)(15806,15823)(15807,15822)(15808,15821)(15809,15820)(15810,15819)(15811,15818)(15812,15817)(15813,15816)(15814,15815)

Polycyclic presentation:

2,31627|b^a=b^31626

Conjugacy classes & character table

15815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(63254, 1);

D31627 #71019308