Finite Group DatabasebetaFinite Group Databasebeta| order | 20042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10021 |
| unambiguous semidirect product | C11⋊D911 |
| unambiguous semidirect product | C911⋊D11 |
| Fitting, socle, derived, Hall | C11×C911 ⋊ C2 |
| Sylow | C911 ⋊ D11 |
| Sylow | C11 ⋊ D911 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C911 | C2 |
| LCS | G ▷ C11×C911 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 922 |
| transitive degree | μt(G) = 10021 |
A minimal faithful permutation representation — 2 generators on 922 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,922)(14,921)(15,920)(16,919)(17,918)(18,917)(19,916)(20,915)(21,914)(22,913)(23,912)(24,911)(25,910)(26,909)(27,908)(28,907)(29,906)(30,905)(31,904)(32,903)(33,902)(34,901)(35,900)(36,899)(37,898)(38,897)(39,896)(40,895)(41,894)(42,893)(43,892)(44,891)(45,890)(46,889)(47,888)(48,887)(49,886)(50,885)(51,884)(52,883)(53,882)(54,881)(55,880)(56,879)(57,878)(58,877)(59,876)(60,875)(61,874)(62,873)(63,872)(64,871)(65,870)(66,869)(67,868)(68,867)(69,866)(70,865)(71,864)(72,863)(73,862)(74,861)(75,860)(76,859)(77,858)(78,857)(79,856)(80,855)(81,854)(82,853)(83,852)(84,851)(85,850)(86,849)(87,848)(88,847)(89,846)(90,845)(91,844)(92,843)(93,842)(94,841)(95,840)(96,839)(97,838)(98,837)(99,836)(100,835)(101,834)(102,833)(103,832)(104,831)(105,830)(106,829)(107,828)(108,827)(109,826)(110,825)(111,824)(112,823)(113,822)(114,821)(115,820)(116,819)(117,818)(118,817)(119,816)(120,815)(121,814)(122,813)(123,812)(124,811)(125,810)(126,809)(127,808)(128,807)(129,806)(130,805)(131,804)(132,803)(133,802)(134,801)(135,800)(136,799)(137,798)(138,797)(139,796)(140,795)(141,794)(142,793)(143,792)(144,791)(145,790)(146,789)(147,788)(148,787)(149,786)(150,785)(151,784)(152,783)(153,782)(154,781)(155,780)(156,779)(157,778)(158,777)(159,776)(160,775)(161,774)(162,773)(163,772)(164,771)(165,770)(166,769)(167,768)(168,767)(169,766)(170,765)(171,764)(172,763)(173,762)(174,761)(175,760)(176,759)(177,758)(178,757)(179,756)(180,755)(181,754)(182,753)(183,752)(184,751)(185,750)(186,749)(187,748)(188,747)(189,746)(190,745)(191,744)(192,743)(193,742)(194,741)(195,740)(196,739)(197,738)(198,737)(199,736)(200,735)(201,734)(202,733)(203,732)(204,731)(205,730)(206,729)(207,728)(208,727)(209,726)(210,725)(211,724)(212,723)(213,722)(214,721)(215,720)(216,719)(217,718)(218,717)(219,716)(220,715)(221,714)(222,713)(223,712)(224,711)(225,710)(226,709)(227,708)(228,707)(229,706)(230,705)(231,704)(232,703)(233,702)(234,701)(235,700)(236,699)(237,698)(238,697)(239,696)(240,695)(241,694)(242,693)(243,692)(244,691)(245,690)(246,689)(247,688)(248,687)(249,686)(250,685)(251,684)(252,683)(253,682)(254,681)(255,680)(256,679)(257,678)(258,677)(259,676)(260,675)(261,674)(262,673)(263,672)(264,671)(265,670)(266,669)(267,668)(268,667)(269,666)(270,665)(271,664)(272,663)(273,662)(274,661)(275,660)(276,659)(277,658)(278,657)(279,656)(280,655)(281,654)(282,653)(283,652)(284,651)(285,650)(286,649)(287,648)(288,647)(289,646)(290,645)(291,644)(292,643)(293,642)(294,641)(295,640)(296,639)(297,638)(298,637)(299,636)(300,635)(301,634)(302,633)(303,632)(304,631)(305,630)(306,629)(307,628)(308,627)(309,626)(310,625)(311,624)(312,623)(313,622)(314,621)(315,620)(316,619)(317,618)(318,617)(319,616)(320,615)(321,614)(322,613)(323,612)(324,611)(325,610)(326,609)(327,608)(328,607)(329,606)(330,605)(331,604)(332,603)(333,602)(334,601)(335,600)(336,599)(337,598)(338,597)(339,596)(340,595)(341,594)(342,593)(343,592)(344,591)(345,590)(346,589)(347,588)(348,587)(349,586)(350,585)(351,584)(352,583)(353,582)(354,581)(355,580)(356,579)(357,578)(358,577)(359,576)(360,575)(361,574)(362,573)(363,572)(364,571)(365,570)(366,569)(367,568)(368,567)(369,566)(370,565)(371,564)(372,563)(373,562)(374,561)(375,560)(376,559)(377,558)(378,557)(379,556)(380,555)(381,554)(382,553)(383,552)(384,551)(385,550)(386,549)(387,548)(388,547)(389,546)(390,545)(391,544)(392,543)(393,542)(394,541)(395,540)(396,539)(397,538)(398,537)(399,536)(400,535)(401,534)(402,533)(403,532)(404,531)(405,530)(406,529)(407,528)(408,527)(409,526)(410,525)(411,524)(412,523)(413,522)(414,521)(415,520)(416,519)(417,518)(418,517)(419,516)(420,515)(421,514)(422,513)(423,512)(424,511)(425,510)(426,509)(427,508)(428,507)(429,506)(430,505)(431,504)(432,503)(433,502)(434,501)(435,500)(436,499)(437,498)(438,497)(439,496)(440,495)(441,494)(442,493)(443,492)(444,491)(445,490)(446,489)(447,488)(448,487)(449,486)(450,485)(451,484)(452,483)(453,482)(454,481)(455,480)(456,479)(457,478)(458,477)(459,476)(460,475)(461,474)(462,473)(463,472)(464,471)(465,470)(466,469)(467,468)Polycyclic presentation:
2,11,911|b^a=b^10,c^a=c^9105012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20042, 3);