Finite Group DatabasebetaFinite Group Databasebeta| order | 34922 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17461 |
| unambiguous semidirect product | C19⋊D919 |
| unambiguous semidirect product | C919⋊D19 |
| Fitting, socle, derived, Hall | C19×C919 ⋊ C2 |
| Sylow | C919 ⋊ D19 |
| Sylow | C19 ⋊ D919 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C919 | C2 |
| LCS | G ▷ C19×C919 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 938 |
| transitive degree | μt(G) = 17461 |
A minimal faithful permutation representation — 2 generators on 938 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);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,938)(22,937)(23,936)(24,935)(25,934)(26,933)(27,932)(28,931)(29,930)(30,929)(31,928)(32,927)(33,926)(34,925)(35,924)(36,923)(37,922)(38,921)(39,920)(40,919)(41,918)(42,917)(43,916)(44,915)(45,914)(46,913)(47,912)(48,911)(49,910)(50,909)(51,908)(52,907)(53,906)(54,905)(55,904)(56,903)(57,902)(58,901)(59,900)(60,899)(61,898)(62,897)(63,896)(64,895)(65,894)(66,893)(67,892)(68,891)(69,890)(70,889)(71,888)(72,887)(73,886)(74,885)(75,884)(76,883)(77,882)(78,881)(79,880)(80,879)(81,878)(82,877)(83,876)(84,875)(85,874)(86,873)(87,872)(88,871)(89,870)(90,869)(91,868)(92,867)(93,866)(94,865)(95,864)(96,863)(97,862)(98,861)(99,860)(100,859)(101,858)(102,857)(103,856)(104,855)(105,854)(106,853)(107,852)(108,851)(109,850)(110,849)(111,848)(112,847)(113,846)(114,845)(115,844)(116,843)(117,842)(118,841)(119,840)(120,839)(121,838)(122,837)(123,836)(124,835)(125,834)(126,833)(127,832)(128,831)(129,830)(130,829)(131,828)(132,827)(133,826)(134,825)(135,824)(136,823)(137,822)(138,821)(139,820)(140,819)(141,818)(142,817)(143,816)(144,815)(145,814)(146,813)(147,812)(148,811)(149,810)(150,809)(151,808)(152,807)(153,806)(154,805)(155,804)(156,803)(157,802)(158,801)(159,800)(160,799)(161,798)(162,797)(163,796)(164,795)(165,794)(166,793)(167,792)(168,791)(169,790)(170,789)(171,788)(172,787)(173,786)(174,785)(175,784)(176,783)(177,782)(178,781)(179,780)(180,779)(181,778)(182,777)(183,776)(184,775)(185,774)(186,773)(187,772)(188,771)(189,770)(190,769)(191,768)(192,767)(193,766)(194,765)(195,764)(196,763)(197,762)(198,761)(199,760)(200,759)(201,758)(202,757)(203,756)(204,755)(205,754)(206,753)(207,752)(208,751)(209,750)(210,749)(211,748)(212,747)(213,746)(214,745)(215,744)(216,743)(217,742)(218,741)(219,740)(220,739)(221,738)(222,737)(223,736)(224,735)(225,734)(226,733)(227,732)(228,731)(229,730)(230,729)(231,728)(232,727)(233,726)(234,725)(235,724)(236,723)(237,722)(238,721)(239,720)(240,719)(241,718)(242,717)(243,716)(244,715)(245,714)(246,713)(247,712)(248,711)(249,710)(250,709)(251,708)(252,707)(253,706)(254,705)(255,704)(256,703)(257,702)(258,701)(259,700)(260,699)(261,698)(262,697)(263,696)(264,695)(265,694)(266,693)(267,692)(268,691)(269,690)(270,689)(271,688)(272,687)(273,686)(274,685)(275,684)(276,683)(277,682)(278,681)(279,680)(280,679)(281,678)(282,677)(283,676)(284,675)(285,674)(286,673)(287,672)(288,671)(289,670)(290,669)(291,668)(292,667)(293,666)(294,665)(295,664)(296,663)(297,662)(298,661)(299,660)(300,659)(301,658)(302,657)(303,656)(304,655)(305,654)(306,653)(307,652)(308,651)(309,650)(310,649)(311,648)(312,647)(313,646)(314,645)(315,644)(316,643)(317,642)(318,641)(319,640)(320,639)(321,638)(322,637)(323,636)(324,635)(325,634)(326,633)(327,632)(328,631)(329,630)(330,629)(331,628)(332,627)(333,626)(334,625)(335,624)(336,623)(337,622)(338,621)(339,620)(340,619)(341,618)(342,617)(343,616)(344,615)(345,614)(346,613)(347,612)(348,611)(349,610)(350,609)(351,608)(352,607)(353,606)(354,605)(355,604)(356,603)(357,602)(358,601)(359,600)(360,599)(361,598)(362,597)(363,596)(364,595)(365,594)(366,593)(367,592)(368,591)(369,590)(370,589)(371,588)(372,587)(373,586)(374,585)(375,584)(376,583)(377,582)(378,581)(379,580)(380,579)(381,578)(382,577)(383,576)(384,575)(385,574)(386,573)(387,572)(388,571)(389,570)(390,569)(391,568)(392,567)(393,566)(394,565)(395,564)(396,563)(397,562)(398,561)(399,560)(400,559)(401,558)(402,557)(403,556)(404,555)(405,554)(406,553)(407,552)(408,551)(409,550)(410,549)(411,548)(412,547)(413,546)(414,545)(415,544)(416,543)(417,542)(418,541)(419,540)(420,539)(421,538)(422,537)(423,536)(424,535)(425,534)(426,533)(427,532)(428,531)(429,530)(430,529)(431,528)(432,527)(433,526)(434,525)(435,524)(436,523)(437,522)(438,521)(439,520)(440,519)(441,518)(442,517)(443,516)(444,515)(445,514)(446,513)(447,512)(448,511)(449,510)(450,509)(451,508)(452,507)(453,506)(454,505)(455,504)(456,503)(457,502)(458,501)(459,500)(460,499)(461,498)(462,497)(463,496)(464,495)(465,494)(466,493)(467,492)(468,491)(469,490)(470,489)(471,488)(472,487)(473,486)(474,485)(475,484)(476,483)(477,482)(478,481)(479,480)Polycyclic presentation:
2,19,919|b^a=b^18,c^a=c^9188732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34922, 3);