D₃₁₃₃₃ #70996363

order	62666
automorphism	Aut(G) order 981725556
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₃₁₃₃₃

Splittings

Fitting, socle, derived, Sylow

C₃₁₃₃₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁₃₃₃	C₂
LCS	G ▷ C₃₁₃₃₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31333
transitive degree	μ_t(G) = 31333

A minimal faithful permutation representation — 2 generators on 31333 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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010)(15326,16009)(15327,16008)(15328,16007)(15329,16006)(15330,16005)(15331,16004)(15332,16003)(15333,16002)(15334,16001)(15335,16000)(15336,15999)(15337,15998)(15338,15997)(15339,15996)(15340,15995)(15341,15994)(15342,15993)(15343,15992)(15344,15991)(15345,15990)(15346,15989)(15347,15988)(15348,15987)(15349,15986)(15350,15985)(15351,15984)(15352,15983)(15353,15982)(15354,15981)(15355,15980)(15356,15979)(15357,15978)(15358,15977)(15359,15976)(15360,15975)(15361,15974)(15362,15973)(15363,15972)(15364,15971)(15365,15970)(15366,15969)(15367,15968)(15368,15967)(15369,15966)(15370,15965)(15371,15964)(15372,15963)(15373,15962)(15374,15961)(15375,15960)(15376,15959)(15377,15958)(15378,15957)(15379,15956)(15380,15955)(15381,15954)(15382,15953)(15383,15952)(15384,15951)(15385,15950)(15386,15949)(15387,15948)(15388,15947)(15389,15946)(15390,15945)(15391,15944)(15392,15943)(15393,15942)(15394,15941)(15395,15940)(15396,15939)(15397,15938)(15398,15937)(15399,15936)(15400,15935)(15401,15934)(15402,15933)(15403,15932)(15404,15931)(15405,15930)(15406,15929)(15407,15928)(15408,15927)(15409,15926)(15410,15925)(15411,15924)(15412,15923)(15413,15922)(15414,15921)(15415,15920)(15416,15919)(15417,15918)(15418,15917)(15419,15916)(15420,15915)(15421,15914)(15422,15913)(15423,15912)(15424,15911)(15425,15910)(15426,15909)(15427,15908)(15428,15907)(15429,15906)(15430,15905)(15431,15904)(15432,15903)(15433,15902)(15434,15901)(15435,15900)(15436,15899)(15437,15898)(15438,15897)(15439,15896)(15440,15895)(15441,15894)(15442,15893)(15443,15892)(15444,15891)(15445,15890)(15446,15889)(15447,15888)(15448,15887)(15449,15886)(15450,15885)(15451,15884)(15452,15883)(15453,15882)(15454,15881)(15455,15880)(15456,15879)(15457,15878)(15458,15877)(15459,15876)(15460,15875)(15461,15874)(15462,15873)(15463,15872)(15464,15871)(15465,15870)(15466,15869)(15467,15868)(15468,15867)(15469,15866)(15470,15865)(15471,15864)(15472,15863)(15473,15862)(15474,15861)(15475,15860)(15476,15859)(15477,15858)(15478,15857)(15479,15856)(15480,15855)(15481,15854)(15482,15853)(15483,15852)(15484,15851)(15485,15850)(15486,15849)(15487,15848)(15488,15847)(15489,15846)(15490,15845)(15491,15844)(15492,15843)(15493,15842)(15494,15841)(15495,15840)(15496,15839)(15497,15838)(15498,15837)(15499,15836)(15500,15835)(15501,15834)(15502,15833)(15503,15832)(15504,15831)(15505,15830)(15506,15829)(15507,15828)(15508,15827)(15509,15826)(15510,15825)(15511,15824)(15512,15823)(15513,15822)(15514,15821)(15515,15820)(15516,15819)(15517,15818)(15518,15817)(15519,15816)(15520,15815)(15521,15814)(15522,15813)(15523,15812)(15524,15811)(15525,15810)(15526,15809)(15527,15808)(15528,15807)(15529,15806)(15530,15805)(15531,15804)(15532,15803)(15533,15802)(15534,15801)(15535,15800)(15536,15799)(15537,15798)(15538,15797)(15539,15796)(15540,15795)(15541,15794)(15542,15793)(15543,15792)(15544,15791)(15545,15790)(15546,15789)(15547,15788)(15548,15787)(15549,15786)(15550,15785)(15551,15784)(15552,15783)(15553,15782)(15554,15781)(15555,15780)(15556,15779)(15557,15778)(15558,15777)(15559,15776)(15560,15775)(15561,15774)(15562,15773)(15563,15772)(15564,15771)(15565,15770)(15566,15769)(15567,15768)(15568,15767)(15569,15766)(15570,15765)(15571,15764)(15572,15763)(15573,15762)(15574,15761)(15575,15760)(15576,15759)(15577,15758)(15578,15757)(15579,15756)(15580,15755)(15581,15754)(15582,15753)(15583,15752)(15584,15751)(15585,15750)(15586,15749)(15587,15748)(15588,15747)(15589,15746)(15590,15745)(15591,15744)(15592,15743)(15593,15742)(15594,15741)(15595,15740)(15596,15739)(15597,15738)(15598,15737)(15599,15736)(15600,15735)(15601,15734)(15602,15733)(15603,15732)(15604,15731)(15605,15730)(15606,15729)(15607,15728)(15608,15727)(15609,15726)(15610,15725)(15611,15724)(15612,15723)(15613,15722)(15614,15721)(15615,15720)(15616,15719)(15617,15718)(15618,15717)(15619,15716)(15620,15715)(15621,15714)(15622,15713)(15623,15712)(15624,15711)(15625,15710)(15626,15709)(15627,15708)(15628,15707)(15629,15706)(15630,15705)(15631,15704)(15632,15703)(15633,15702)(15634,15701)(15635,15700)(15636,15699)(15637,15698)(15638,15697)(15639,15696)(15640,15695)(15641,15694)(15642,15693)(15643,15692)(15644,15691)(15645,15690)(15646,15689)(15647,15688)(15648,15687)(15649,15686)(15650,15685)(15651,15684)(15652,15683)(15653,15682)(15654,15681)(15655,15680)(15656,15679)(15657,15678)(15658,15677)(15659,15676)(15660,15675)(15661,15674)(15662,15673)(15663,15672)(15664,15671)(15665,15670)(15666,15669)(15667,15668)

Polycyclic presentation:

2,31333|b^a=b^31332

Conjugacy classes & character table

15668 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(62666, 1);

D31333 #70996363