Finite Group DatabasebetaFinite Group Databasebeta| order | 35986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17993 |
| unambiguous semidirect product | C19⋊D947 |
| unambiguous semidirect product | C947⋊D19 |
| Fitting, socle, derived, Hall | C19×C947 ⋊ C2 |
| Sylow | C947 ⋊ D19 |
| Sylow | C19 ⋊ D947 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C947 | C2 |
| LCS | G ▷ C19×C947 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 966 |
| transitive degree | μt(G) = 17993 |
A minimal faithful permutation representation — 2 generators on 966 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);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,966)(22,965)(23,964)(24,963)(25,962)(26,961)(27,960)(28,959)(29,958)(30,957)(31,956)(32,955)(33,954)(34,953)(35,952)(36,951)(37,950)(38,949)(39,948)(40,947)(41,946)(42,945)(43,944)(44,943)(45,942)(46,941)(47,940)(48,939)(49,938)(50,937)(51,936)(52,935)(53,934)(54,933)(55,932)(56,931)(57,930)(58,929)(59,928)(60,927)(61,926)(62,925)(63,924)(64,923)(65,922)(66,921)(67,920)(68,919)(69,918)(70,917)(71,916)(72,915)(73,914)(74,913)(75,912)(76,911)(77,910)(78,909)(79,908)(80,907)(81,906)(82,905)(83,904)(84,903)(85,902)(86,901)(87,900)(88,899)(89,898)(90,897)(91,896)(92,895)(93,894)(94,893)(95,892)(96,891)(97,890)(98,889)(99,888)(100,887)(101,886)(102,885)(103,884)(104,883)(105,882)(106,881)(107,880)(108,879)(109,878)(110,877)(111,876)(112,875)(113,874)(114,873)(115,872)(116,871)(117,870)(118,869)(119,868)(120,867)(121,866)(122,865)(123,864)(124,863)(125,862)(126,861)(127,860)(128,859)(129,858)(130,857)(131,856)(132,855)(133,854)(134,853)(135,852)(136,851)(137,850)(138,849)(139,848)(140,847)(141,846)(142,845)(143,844)(144,843)(145,842)(146,841)(147,840)(148,839)(149,838)(150,837)(151,836)(152,835)(153,834)(154,833)(155,832)(156,831)(157,830)(158,829)(159,828)(160,827)(161,826)(162,825)(163,824)(164,823)(165,822)(166,821)(167,820)(168,819)(169,818)(170,817)(171,816)(172,815)(173,814)(174,813)(175,812)(176,811)(177,810)(178,809)(179,808)(180,807)(181,806)(182,805)(183,804)(184,803)(185,802)(186,801)(187,800)(188,799)(189,798)(190,797)(191,796)(192,795)(193,794)(194,793)(195,792)(196,791)(197,790)(198,789)(199,788)(200,787)(201,786)(202,785)(203,784)(204,783)(205,782)(206,781)(207,780)(208,779)(209,778)(210,777)(211,776)(212,775)(213,774)(214,773)(215,772)(216,771)(217,770)(218,769)(219,768)(220,767)(221,766)(222,765)(223,764)(224,763)(225,762)(226,761)(227,760)(228,759)(229,758)(230,757)(231,756)(232,755)(233,754)(234,753)(235,752)(236,751)(237,750)(238,749)(239,748)(240,747)(241,746)(242,745)(243,744)(244,743)(245,742)(246,741)(247,740)(248,739)(249,738)(250,737)(251,736)(252,735)(253,734)(254,733)(255,732)(256,731)(257,730)(258,729)(259,728)(260,727)(261,726)(262,725)(263,724)(264,723)(265,722)(266,721)(267,720)(268,719)(269,718)(270,717)(271,716)(272,715)(273,714)(274,713)(275,712)(276,711)(277,710)(278,709)(279,708)(280,707)(281,706)(282,705)(283,704)(284,703)(285,702)(286,701)(287,700)(288,699)(289,698)(290,697)(291,696)(292,695)(293,694)(294,693)(295,692)(296,691)(297,690)(298,689)(299,688)(300,687)(301,686)(302,685)(303,684)(304,683)(305,682)(306,681)(307,680)(308,679)(309,678)(310,677)(311,676)(312,675)(313,674)(314,673)(315,672)(316,671)(317,670)(318,669)(319,668)(320,667)(321,666)(322,665)(323,664)(324,663)(325,662)(326,661)(327,660)(328,659)(329,658)(330,657)(331,656)(332,655)(333,654)(334,653)(335,652)(336,651)(337,650)(338,649)(339,648)(340,647)(341,646)(342,645)(343,644)(344,643)(345,642)(346,641)(347,640)(348,639)(349,638)(350,637)(351,636)(352,635)(353,634)(354,633)(355,632)(356,631)(357,630)(358,629)(359,628)(360,627)(361,626)(362,625)(363,624)(364,623)(365,622)(366,621)(367,620)(368,619)(369,618)(370,617)(371,616)(372,615)(373,614)(374,613)(375,612)(376,611)(377,610)(378,609)(379,608)(380,607)(381,606)(382,605)(383,604)(384,603)(385,602)(386,601)(387,600)(388,599)(389,598)(390,597)(391,596)(392,595)(393,594)(394,593)(395,592)(396,591)(397,590)(398,589)(399,588)(400,587)(401,586)(402,585)(403,584)(404,583)(405,582)(406,581)(407,580)(408,579)(409,578)(410,577)(411,576)(412,575)(413,574)(414,573)(415,572)(416,571)(417,570)(418,569)(419,568)(420,567)(421,566)(422,565)(423,564)(424,563)(425,562)(426,561)(427,560)(428,559)(429,558)(430,557)(431,556)(432,555)(433,554)(434,553)(435,552)(436,551)(437,550)(438,549)(439,548)(440,547)(441,546)(442,545)(443,544)(444,543)(445,542)(446,541)(447,540)(448,539)(449,538)(450,537)(451,536)(452,535)(453,534)(454,533)(455,532)(456,531)(457,530)(458,529)(459,528)(460,527)(461,526)(462,525)(463,524)(464,523)(465,522)(466,521)(467,520)(468,519)(469,518)(470,517)(471,516)(472,515)(473,514)(474,513)(475,512)(476,511)(477,510)(478,509)(479,508)(480,507)(481,506)(482,505)(483,504)(484,503)(485,502)(486,501)(487,500)(488,499)(489,498)(490,497)(491,496)(492,495)(493,494)Polycyclic presentation:
2,19,947|b^a=b^18,c^a=c^9468998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35986, 3);