Finite Group DatabasebetaFinite Group Databasebeta| order | 36346 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18173 |
| unambiguous semidirect product | C17⋊D1069 |
| unambiguous semidirect product | C1069⋊D17 |
| Fitting, socle, derived, Hall | C17×C1069 ⋊ C2 |
| Sylow | C1069 ⋊ D17 |
| Sylow | C17 ⋊ D1069 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C1069 | C2 |
| LCS | G ▷ C17×C1069 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1086 |
| transitive degree | μt(G) = 18173 |
A minimal faithful permutation representation — 2 generators on 1086 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,1086)(20,1085)(21,1084)(22,1083)(23,1082)(24,1081)(25,1080)(26,1079)(27,1078)(28,1077)(29,1076)(30,1075)(31,1074)(32,1073)(33,1072)(34,1071)(35,1070)(36,1069)(37,1068)(38,1067)(39,1066)(40,1065)(41,1064)(42,1063)(43,1062)(44,1061)(45,1060)(46,1059)(47,1058)(48,1057)(49,1056)(50,1055)(51,1054)(52,1053)(53,1052)(54,1051)(55,1050)(56,1049)(57,1048)(58,1047)(59,1046)(60,1045)(61,1044)(62,1043)(63,1042)(64,1041)(65,1040)(66,1039)(67,1038)(68,1037)(69,1036)(70,1035)(71,1034)(72,1033)(73,1032)(74,1031)(75,1030)(76,1029)(77,1028)(78,1027)(79,1026)(80,1025)(81,1024)(82,1023)(83,1022)(84,1021)(85,1020)(86,1019)(87,1018)(88,1017)(89,1016)(90,1015)(91,1014)(92,1013)(93,1012)(94,1011)(95,1010)(96,1009)(97,1008)(98,1007)(99,1006)(100,1005)(101,1004)(102,1003)(103,1002)(104,1001)(105,1000)(106,999)(107,998)(108,997)(109,996)(110,995)(111,994)(112,993)(113,992)(114,991)(115,990)(116,989)(117,988)(118,987)(119,986)(120,985)(121,984)(122,983)(123,982)(124,981)(125,980)(126,979)(127,978)(128,977)(129,976)(130,975)(131,974)(132,973)(133,972)(134,971)(135,970)(136,969)(137,968)(138,967)(139,966)(140,965)(141,964)(142,963)(143,962)(144,961)(145,960)(146,959)(147,958)(148,957)(149,956)(150,955)(151,954)(152,953)(153,952)(154,951)(155,950)(156,949)(157,948)(158,947)(159,946)(160,945)(161,944)(162,943)(163,942)(164,941)(165,940)(166,939)(167,938)(168,937)(169,936)(170,935)(171,934)(172,933)(173,932)(174,931)(175,930)(176,929)(177,928)(178,927)(179,926)(180,925)(181,924)(182,923)(183,922)(184,921)(185,920)(186,919)(187,918)(188,917)(189,916)(190,915)(191,914)(192,913)(193,912)(194,911)(195,910)(196,909)(197,908)(198,907)(199,906)(200,905)(201,904)(202,903)(203,902)(204,901)(205,900)(206,899)(207,898)(208,897)(209,896)(210,895)(211,894)(212,893)(213,892)(214,891)(215,890)(216,889)(217,888)(218,887)(219,886)(220,885)(221,884)(222,883)(223,882)(224,881)(225,880)(226,879)(227,878)(228,877)(229,876)(230,875)(231,874)(232,873)(233,872)(234,871)(235,870)(236,869)(237,868)(238,867)(239,866)(240,865)(241,864)(242,863)(243,862)(244,861)(245,860)(246,859)(247,858)(248,857)(249,856)(250,855)(251,854)(252,853)(253,852)(254,851)(255,850)(256,849)(257,848)(258,847)(259,846)(260,845)(261,844)(262,843)(263,842)(264,841)(265,840)(266,839)(267,838)(268,837)(269,836)(270,835)(271,834)(272,833)(273,832)(274,831)(275,830)(276,829)(277,828)(278,827)(279,826)(280,825)(281,824)(282,823)(283,822)(284,821)(285,820)(286,819)(287,818)(288,817)(289,816)(290,815)(291,814)(292,813)(293,812)(294,811)(295,810)(296,809)(297,808)(298,807)(299,806)(300,805)(301,804)(302,803)(303,802)(304,801)(305,800)(306,799)(307,798)(308,797)(309,796)(310,795)(311,794)(312,793)(313,792)(314,791)(315,790)(316,789)(317,788)(318,787)(319,786)(320,785)(321,784)(322,783)(323,782)(324,781)(325,780)(326,779)(327,778)(328,777)(329,776)(330,775)(331,774)(332,773)(333,772)(334,771)(335,770)(336,769)(337,768)(338,767)(339,766)(340,765)(341,764)(342,763)(343,762)(344,761)(345,760)(346,759)(347,758)(348,757)(349,756)(350,755)(351,754)(352,753)(353,752)(354,751)(355,750)(356,749)(357,748)(358,747)(359,746)(360,745)(361,744)(362,743)(363,742)(364,741)(365,740)(366,739)(367,738)(368,737)(369,736)(370,735)(371,734)(372,733)(373,732)(374,731)(375,730)(376,729)(377,728)(378,727)(379,726)(380,725)(381,724)(382,723)(383,722)(384,721)(385,720)(386,719)(387,718)(388,717)(389,716)(390,715)(391,714)(392,713)(393,712)(394,711)(395,710)(396,709)(397,708)(398,707)(399,706)(400,705)(401,704)(402,703)(403,702)(404,701)(405,700)(406,699)(407,698)(408,697)(409,696)(410,695)(411,694)(412,693)(413,692)(414,691)(415,690)(416,689)(417,688)(418,687)(419,686)(420,685)(421,684)(422,683)(423,682)(424,681)(425,680)(426,679)(427,678)(428,677)(429,676)(430,675)(431,674)(432,673)(433,672)(434,671)(435,670)(436,669)(437,668)(438,667)(439,666)(440,665)(441,664)(442,663)(443,662)(444,661)(445,660)(446,659)(447,658)(448,657)(449,656)(450,655)(451,654)(452,653)(453,652)(454,651)(455,650)(456,649)(457,648)(458,647)(459,646)(460,645)(461,644)(462,643)(463,642)(464,641)(465,640)(466,639)(467,638)(468,637)(469,636)(470,635)(471,634)(472,633)(473,632)(474,631)(475,630)(476,629)(477,628)(478,627)(479,626)(480,625)(481,624)(482,623)(483,622)(484,621)(485,620)(486,619)(487,618)(488,617)(489,616)(490,615)(491,614)(492,613)(493,612)(494,611)(495,610)(496,609)(497,608)(498,607)(499,606)(500,605)(501,604)(502,603)(503,602)(504,601)(505,600)(506,599)(507,598)(508,597)(509,596)(510,595)(511,594)(512,593)(513,592)(514,591)(515,590)(516,589)(517,588)(518,587)(519,586)(520,585)(521,584)(522,583)(523,582)(524,581)(525,580)(526,579)(527,578)(528,577)(529,576)(530,575)(531,574)(532,573)(533,572)(534,571)(535,570)(536,569)(537,568)(538,567)(539,566)(540,565)(541,564)(542,563)(543,562)(544,561)(545,560)(546,559)(547,558)(548,557)(549,556)(550,555)(551,554)(552,553)Polycyclic presentation:
2,17,1069|b^a=b^16,c^a=c^10689088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36346, 3);