Finite Group DatabasebetaFinite Group Databasebeta| order | 19426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9713 |
| unambiguous semidirect product | C11⋊D883 |
| unambiguous semidirect product | C883⋊D11 |
| Fitting, socle, derived, Hall | C11×C883 ⋊ C2 |
| Sylow | C883 ⋊ D11 |
| Sylow | C11 ⋊ D883 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C883 | C2 |
| LCS | G ▷ C11×C883 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 894 |
| transitive degree | μt(G) = 9713 |
A minimal faithful permutation representation — 2 generators on 894 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,894)(14,893)(15,892)(16,891)(17,890)(18,889)(19,888)(20,887)(21,886)(22,885)(23,884)(24,883)(25,882)(26,881)(27,880)(28,879)(29,878)(30,877)(31,876)(32,875)(33,874)(34,873)(35,872)(36,871)(37,870)(38,869)(39,868)(40,867)(41,866)(42,865)(43,864)(44,863)(45,862)(46,861)(47,860)(48,859)(49,858)(50,857)(51,856)(52,855)(53,854)(54,853)(55,852)(56,851)(57,850)(58,849)(59,848)(60,847)(61,846)(62,845)(63,844)(64,843)(65,842)(66,841)(67,840)(68,839)(69,838)(70,837)(71,836)(72,835)(73,834)(74,833)(75,832)(76,831)(77,830)(78,829)(79,828)(80,827)(81,826)(82,825)(83,824)(84,823)(85,822)(86,821)(87,820)(88,819)(89,818)(90,817)(91,816)(92,815)(93,814)(94,813)(95,812)(96,811)(97,810)(98,809)(99,808)(100,807)(101,806)(102,805)(103,804)(104,803)(105,802)(106,801)(107,800)(108,799)(109,798)(110,797)(111,796)(112,795)(113,794)(114,793)(115,792)(116,791)(117,790)(118,789)(119,788)(120,787)(121,786)(122,785)(123,784)(124,783)(125,782)(126,781)(127,780)(128,779)(129,778)(130,777)(131,776)(132,775)(133,774)(134,773)(135,772)(136,771)(137,770)(138,769)(139,768)(140,767)(141,766)(142,765)(143,764)(144,763)(145,762)(146,761)(147,760)(148,759)(149,758)(150,757)(151,756)(152,755)(153,754)(154,753)(155,752)(156,751)(157,750)(158,749)(159,748)(160,747)(161,746)(162,745)(163,744)(164,743)(165,742)(166,741)(167,740)(168,739)(169,738)(170,737)(171,736)(172,735)(173,734)(174,733)(175,732)(176,731)(177,730)(178,729)(179,728)(180,727)(181,726)(182,725)(183,724)(184,723)(185,722)(186,721)(187,720)(188,719)(189,718)(190,717)(191,716)(192,715)(193,714)(194,713)(195,712)(196,711)(197,710)(198,709)(199,708)(200,707)(201,706)(202,705)(203,704)(204,703)(205,702)(206,701)(207,700)(208,699)(209,698)(210,697)(211,696)(212,695)(213,694)(214,693)(215,692)(216,691)(217,690)(218,689)(219,688)(220,687)(221,686)(222,685)(223,684)(224,683)(225,682)(226,681)(227,680)(228,679)(229,678)(230,677)(231,676)(232,675)(233,674)(234,673)(235,672)(236,671)(237,670)(238,669)(239,668)(240,667)(241,666)(242,665)(243,664)(244,663)(245,662)(246,661)(247,660)(248,659)(249,658)(250,657)(251,656)(252,655)(253,654)(254,653)(255,652)(256,651)(257,650)(258,649)(259,648)(260,647)(261,646)(262,645)(263,644)(264,643)(265,642)(266,641)(267,640)(268,639)(269,638)(270,637)(271,636)(272,635)(273,634)(274,633)(275,632)(276,631)(277,630)(278,629)(279,628)(280,627)(281,626)(282,625)(283,624)(284,623)(285,622)(286,621)(287,620)(288,619)(289,618)(290,617)(291,616)(292,615)(293,614)(294,613)(295,612)(296,611)(297,610)(298,609)(299,608)(300,607)(301,606)(302,605)(303,604)(304,603)(305,602)(306,601)(307,600)(308,599)(309,598)(310,597)(311,596)(312,595)(313,594)(314,593)(315,592)(316,591)(317,590)(318,589)(319,588)(320,587)(321,586)(322,585)(323,584)(324,583)(325,582)(326,581)(327,580)(328,579)(329,578)(330,577)(331,576)(332,575)(333,574)(334,573)(335,572)(336,571)(337,570)(338,569)(339,568)(340,567)(341,566)(342,565)(343,564)(344,563)(345,562)(346,561)(347,560)(348,559)(349,558)(350,557)(351,556)(352,555)(353,554)(354,553)(355,552)(356,551)(357,550)(358,549)(359,548)(360,547)(361,546)(362,545)(363,544)(364,543)(365,542)(366,541)(367,540)(368,539)(369,538)(370,537)(371,536)(372,535)(373,534)(374,533)(375,532)(376,531)(377,530)(378,529)(379,528)(380,527)(381,526)(382,525)(383,524)(384,523)(385,522)(386,521)(387,520)(388,519)(389,518)(390,517)(391,516)(392,515)(393,514)(394,513)(395,512)(396,511)(397,510)(398,509)(399,508)(400,507)(401,506)(402,505)(403,504)(404,503)(405,502)(406,501)(407,500)(408,499)(409,498)(410,497)(411,496)(412,495)(413,494)(414,493)(415,492)(416,491)(417,490)(418,489)(419,488)(420,487)(421,486)(422,485)(423,484)(424,483)(425,482)(426,481)(427,480)(428,479)(429,478)(430,477)(431,476)(432,475)(433,474)(434,473)(435,472)(436,471)(437,470)(438,469)(439,468)(440,467)(441,466)(442,465)(443,464)(444,463)(445,462)(446,461)(447,460)(448,459)(449,458)(450,457)(451,456)(452,455)(453,454)Polycyclic presentation:
2,11,883|b^a=b^10,c^a=c^8824858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19426, 3);