D₃₁₀₆₃ #70971920

order	62126
automorphism	Aut(G) order 964878906
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₃₁₀₆₃

Splittings

Fitting, socle, derived, Sylow

C₃₁₀₆₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁₀₆₃	C₂
LCS	G ▷ C₃₁₀₆₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31063
transitive degree	μ_t(G) = 31063

A minimal faithful permutation representation — 2 generators on 31063 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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000)(15066,15999)(15067,15998)(15068,15997)(15069,15996)(15070,15995)(15071,15994)(15072,15993)(15073,15992)(15074,15991)(15075,15990)(15076,15989)(15077,15988)(15078,15987)(15079,15986)(15080,15985)(15081,15984)(15082,15983)(15083,15982)(15084,15981)(15085,15980)(15086,15979)(15087,15978)(15088,15977)(15089,15976)(15090,15975)(15091,15974)(15092,15973)(15093,15972)(15094,15971)(15095,15970)(15096,15969)(15097,15968)(15098,15967)(15099,15966)(15100,15965)(15101,15964)(15102,15963)(15103,15962)(15104,15961)(15105,15960)(15106,15959)(15107,15958)(15108,15957)(15109,15956)(15110,15955)(15111,15954)(15112,15953)(15113,15952)(15114,15951)(15115,15950)(15116,15949)(15117,15948)(15118,15947)(15119,15946)(15120,15945)(15121,15944)(15122,15943)(15123,15942)(15124,15941)(15125,15940)(15126,15939)(15127,15938)(15128,15937)(15129,15936)(15130,15935)(15131,15934)(15132,15933)(15133,15932)(15134,15931)(15135,15930)(15136,15929)(15137,15928)(15138,15927)(15139,15926)(15140,15925)(15141,15924)(15142,15923)(15143,15922)(15144,15921)(15145,15920)(15146,15919)(15147,15918)(15148,15917)(15149,15916)(15150,15915)(15151,15914)(15152,15913)(15153,15912)(15154,15911)(15155,15910)(15156,15909)(15157,15908)(15158,15907)(15159,15906)(15160,15905)(15161,15904)(15162,15903)(15163,15902)(15164,15901)(15165,15900)(15166,15899)(15167,15898)(15168,15897)(15169,15896)(15170,15895)(15171,15894)(15172,15893)(15173,15892)(15174,15891)(15175,15890)(15176,15889)(15177,15888)(15178,15887)(15179,15886)(15180,15885)(15181,15884)(15182,15883)(15183,15882)(15184,15881)(15185,15880)(15186,15879)(15187,15878)(15188,15877)(15189,15876)(15190,15875)(15191,15874)(15192,15873)(15193,15872)(15194,15871)(15195,15870)(15196,15869)(15197,15868)(15198,15867)(15199,15866)(15200,15865)(15201,15864)(15202,15863)(15203,15862)(15204,15861)(15205,15860)(15206,15859)(15207,15858)(15208,15857)(15209,15856)(15210,15855)(15211,15854)(15212,15853)(15213,15852)(15214,15851)(15215,15850)(15216,15849)(15217,15848)(15218,15847)(15219,15846)(15220,15845)(15221,15844)(15222,15843)(15223,15842)(15224,15841)(15225,15840)(15226,15839)(15227,15838)(15228,15837)(15229,15836)(15230,15835)(15231,15834)(15232,15833)(15233,15832)(15234,15831)(15235,15830)(15236,15829)(15237,15828)(15238,15827)(15239,15826)(15240,15825)(15241,15824)(15242,15823)(15243,15822)(15244,15821)(15245,15820)(15246,15819)(15247,15818)(15248,15817)(15249,15816)(15250,15815)(15251,15814)(15252,15813)(15253,15812)(15254,15811)(15255,15810)(15256,15809)(15257,15808)(15258,15807)(15259,15806)(15260,15805)(15261,15804)(15262,15803)(15263,15802)(15264,15801)(15265,15800)(15266,15799)(15267,15798)(15268,15797)(15269,15796)(15270,15795)(15271,15794)(15272,15793)(15273,15792)(15274,15791)(15275,15790)(15276,15789)(15277,15788)(15278,15787)(15279,15786)(15280,15785)(15281,15784)(15282,15783)(15283,15782)(15284,15781)(15285,15780)(15286,15779)(15287,15778)(15288,15777)(15289,15776)(15290,15775)(15291,15774)(15292,15773)(15293,15772)(15294,15771)(15295,15770)(15296,15769)(15297,15768)(15298,15767)(15299,15766)(15300,15765)(15301,15764)(15302,15763)(15303,15762)(15304,15761)(15305,15760)(15306,15759)(15307,15758)(15308,15757)(15309,15756)(15310,15755)(15311,15754)(15312,15753)(15313,15752)(15314,15751)(15315,15750)(15316,15749)(15317,15748)(15318,15747)(15319,15746)(15320,15745)(15321,15744)(15322,15743)(15323,15742)(15324,15741)(15325,15740)(15326,15739)(15327,15738)(15328,15737)(15329,15736)(15330,15735)(15331,15734)(15332,15733)(15333,15732)(15334,15731)(15335,15730)(15336,15729)(15337,15728)(15338,15727)(15339,15726)(15340,15725)(15341,15724)(15342,15723)(15343,15722)(15344,15721)(15345,15720)(15346,15719)(15347,15718)(15348,15717)(15349,15716)(15350,15715)(15351,15714)(15352,15713)(15353,15712)(15354,15711)(15355,15710)(15356,15709)(15357,15708)(15358,15707)(15359,15706)(15360,15705)(15361,15704)(15362,15703)(15363,15702)(15364,15701)(15365,15700)(15366,15699)(15367,15698)(15368,15697)(15369,15696)(15370,15695)(15371,15694)(15372,15693)(15373,15692)(15374,15691)(15375,15690)(15376,15689)(15377,15688)(15378,15687)(15379,15686)(15380,15685)(15381,15684)(15382,15683)(15383,15682)(15384,15681)(15385,15680)(15386,15679)(15387,15678)(15388,15677)(15389,15676)(15390,15675)(15391,15674)(15392,15673)(15393,15672)(15394,15671)(15395,15670)(15396,15669)(15397,15668)(15398,15667)(15399,15666)(15400,15665)(15401,15664)(15402,15663)(15403,15662)(15404,15661)(15405,15660)(15406,15659)(15407,15658)(15408,15657)(15409,15656)(15410,15655)(15411,15654)(15412,15653)(15413,15652)(15414,15651)(15415,15650)(15416,15649)(15417,15648)(15418,15647)(15419,15646)(15420,15645)(15421,15644)(15422,15643)(15423,15642)(15424,15641)(15425,15640)(15426,15639)(15427,15638)(15428,15637)(15429,15636)(15430,15635)(15431,15634)(15432,15633)(15433,15632)(15434,15631)(15435,15630)(15436,15629)(15437,15628)(15438,15627)(15439,15626)(15440,15625)(15441,15624)(15442,15623)(15443,15622)(15444,15621)(15445,15620)(15446,15619)(15447,15618)(15448,15617)(15449,15616)(154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Polycyclic presentation:

2,31063|b^a=b^31062

Conjugacy classes & character table

15533 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(62126, 1);

D31063 #70971920