Finite Group DatabasebetaFinite Group Databasebeta| order | 20218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10109 |
| unambiguous semidirect product | C11⋊D919 |
| unambiguous semidirect product | C919⋊D11 |
| Fitting, socle, derived, Hall | C11×C919 ⋊ C2 |
| Sylow | C919 ⋊ D11 |
| Sylow | C11 ⋊ D919 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C919 | C2 |
| LCS | G ▷ C11×C919 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 930 |
| transitive degree | μt(G) = 10109 |
A minimal faithful permutation representation — 2 generators on 930 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,930)(14,929)(15,928)(16,927)(17,926)(18,925)(19,924)(20,923)(21,922)(22,921)(23,920)(24,919)(25,918)(26,917)(27,916)(28,915)(29,914)(30,913)(31,912)(32,911)(33,910)(34,909)(35,908)(36,907)(37,906)(38,905)(39,904)(40,903)(41,902)(42,901)(43,900)(44,899)(45,898)(46,897)(47,896)(48,895)(49,894)(50,893)(51,892)(52,891)(53,890)(54,889)(55,888)(56,887)(57,886)(58,885)(59,884)(60,883)(61,882)(62,881)(63,880)(64,879)(65,878)(66,877)(67,876)(68,875)(69,874)(70,873)(71,872)(72,871)(73,870)(74,869)(75,868)(76,867)(77,866)(78,865)(79,864)(80,863)(81,862)(82,861)(83,860)(84,859)(85,858)(86,857)(87,856)(88,855)(89,854)(90,853)(91,852)(92,851)(93,850)(94,849)(95,848)(96,847)(97,846)(98,845)(99,844)(100,843)(101,842)(102,841)(103,840)(104,839)(105,838)(106,837)(107,836)(108,835)(109,834)(110,833)(111,832)(112,831)(113,830)(114,829)(115,828)(116,827)(117,826)(118,825)(119,824)(120,823)(121,822)(122,821)(123,820)(124,819)(125,818)(126,817)(127,816)(128,815)(129,814)(130,813)(131,812)(132,811)(133,810)(134,809)(135,808)(136,807)(137,806)(138,805)(139,804)(140,803)(141,802)(142,801)(143,800)(144,799)(145,798)(146,797)(147,796)(148,795)(149,794)(150,793)(151,792)(152,791)(153,790)(154,789)(155,788)(156,787)(157,786)(158,785)(159,784)(160,783)(161,782)(162,781)(163,780)(164,779)(165,778)(166,777)(167,776)(168,775)(169,774)(170,773)(171,772)(172,771)(173,770)(174,769)(175,768)(176,767)(177,766)(178,765)(179,764)(180,763)(181,762)(182,761)(183,760)(184,759)(185,758)(186,757)(187,756)(188,755)(189,754)(190,753)(191,752)(192,751)(193,750)(194,749)(195,748)(196,747)(197,746)(198,745)(199,744)(200,743)(201,742)(202,741)(203,740)(204,739)(205,738)(206,737)(207,736)(208,735)(209,734)(210,733)(211,732)(212,731)(213,730)(214,729)(215,728)(216,727)(217,726)(218,725)(219,724)(220,723)(221,722)(222,721)(223,720)(224,719)(225,718)(226,717)(227,716)(228,715)(229,714)(230,713)(231,712)(232,711)(233,710)(234,709)(235,708)(236,707)(237,706)(238,705)(239,704)(240,703)(241,702)(242,701)(243,700)(244,699)(245,698)(246,697)(247,696)(248,695)(249,694)(250,693)(251,692)(252,691)(253,690)(254,689)(255,688)(256,687)(257,686)(258,685)(259,684)(260,683)(261,682)(262,681)(263,680)(264,679)(265,678)(266,677)(267,676)(268,675)(269,674)(270,673)(271,672)(272,671)(273,670)(274,669)(275,668)(276,667)(277,666)(278,665)(279,664)(280,663)(281,662)(282,661)(283,660)(284,659)(285,658)(286,657)(287,656)(288,655)(289,654)(290,653)(291,652)(292,651)(293,650)(294,649)(295,648)(296,647)(297,646)(298,645)(299,644)(300,643)(301,642)(302,641)(303,640)(304,639)(305,638)(306,637)(307,636)(308,635)(309,634)(310,633)(311,632)(312,631)(313,630)(314,629)(315,628)(316,627)(317,626)(318,625)(319,624)(320,623)(321,622)(322,621)(323,620)(324,619)(325,618)(326,617)(327,616)(328,615)(329,614)(330,613)(331,612)(332,611)(333,610)(334,609)(335,608)(336,607)(337,606)(338,605)(339,604)(340,603)(341,602)(342,601)(343,600)(344,599)(345,598)(346,597)(347,596)(348,595)(349,594)(350,593)(351,592)(352,591)(353,590)(354,589)(355,588)(356,587)(357,586)(358,585)(359,584)(360,583)(361,582)(362,581)(363,580)(364,579)(365,578)(366,577)(367,576)(368,575)(369,574)(370,573)(371,572)(372,571)(373,570)(374,569)(375,568)(376,567)(377,566)(378,565)(379,564)(380,563)(381,562)(382,561)(383,560)(384,559)(385,558)(386,557)(387,556)(388,555)(389,554)(390,553)(391,552)(392,551)(393,550)(394,549)(395,548)(396,547)(397,546)(398,545)(399,544)(400,543)(401,542)(402,541)(403,540)(404,539)(405,538)(406,537)(407,536)(408,535)(409,534)(410,533)(411,532)(412,531)(413,530)(414,529)(415,528)(416,527)(417,526)(418,525)(419,524)(420,523)(421,522)(422,521)(423,520)(424,519)(425,518)(426,517)(427,516)(428,515)(429,514)(430,513)(431,512)(432,511)(433,510)(434,509)(435,508)(436,507)(437,506)(438,505)(439,504)(440,503)(441,502)(442,501)(443,500)(444,499)(445,498)(446,497)(447,496)(448,495)(449,494)(450,493)(451,492)(452,491)(453,490)(454,489)(455,488)(456,487)(457,486)(458,485)(459,484)(460,483)(461,482)(462,481)(463,480)(464,479)(465,478)(466,477)(467,476)(468,475)(469,474)(470,473)(471,472)Polycyclic presentation:
2,11,919|b^a=b^10,c^a=c^9185056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20218, 3);