Finite Group DatabasebetaFinite Group Databasebeta| order | 36212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9053 |
| unambiguous semidirect product | C11⋊Dic823 |
| unambiguous semidirect product | C823⋊Dic11 |
| derived, Hall | C11×C823 ⋊ C4 |
| Sylow | C823 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic823 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9053 |
| commutator, hypocenter | C11×C823 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C823 | C2 |
| LCS | G ▷ C11×C823 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 838 |
| transitive degree | μt(G) = 36212 |
A minimal faithful permutation representation — 2 generators on 838 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,838)(18,837)(19,836)(20,835)(21,834)(22,833)(23,832)(24,831)(25,830)(26,829)(27,828)(28,827)(29,826)(30,825)(31,824)(32,823)(33,822)(34,821)(35,820)(36,819)(37,818)(38,817)(39,816)(40,815)(41,814)(42,813)(43,812)(44,811)(45,810)(46,809)(47,808)(48,807)(49,806)(50,805)(51,804)(52,803)(53,802)(54,801)(55,800)(56,799)(57,798)(58,797)(59,796)(60,795)(61,794)(62,793)(63,792)(64,791)(65,790)(66,789)(67,788)(68,787)(69,786)(70,785)(71,784)(72,783)(73,782)(74,781)(75,780)(76,779)(77,778)(78,777)(79,776)(80,775)(81,774)(82,773)(83,772)(84,771)(85,770)(86,769)(87,768)(88,767)(89,766)(90,765)(91,764)(92,763)(93,762)(94,761)(95,760)(96,759)(97,758)(98,757)(99,756)(100,755)(101,754)(102,753)(103,752)(104,751)(105,750)(106,749)(107,748)(108,747)(109,746)(110,745)(111,744)(112,743)(113,742)(114,741)(115,740)(116,739)(117,738)(118,737)(119,736)(120,735)(121,734)(122,733)(123,732)(124,731)(125,730)(126,729)(127,728)(128,727)(129,726)(130,725)(131,724)(132,723)(133,722)(134,721)(135,720)(136,719)(137,718)(138,717)(139,716)(140,715)(141,714)(142,713)(143,712)(144,711)(145,710)(146,709)(147,708)(148,707)(149,706)(150,705)(151,704)(152,703)(153,702)(154,701)(155,700)(156,699)(157,698)(158,697)(159,696)(160,695)(161,694)(162,693)(163,692)(164,691)(165,690)(166,689)(167,688)(168,687)(169,686)(170,685)(171,684)(172,683)(173,682)(174,681)(175,680)(176,679)(177,678)(178,677)(179,676)(180,675)(181,674)(182,673)(183,672)(184,671)(185,670)(186,669)(187,668)(188,667)(189,666)(190,665)(191,664)(192,663)(193,662)(194,661)(195,660)(196,659)(197,658)(198,657)(199,656)(200,655)(201,654)(202,653)(203,652)(204,651)(205,650)(206,649)(207,648)(208,647)(209,646)(210,645)(211,644)(212,643)(213,642)(214,641)(215,640)(216,639)(217,638)(218,637)(219,636)(220,635)(221,634)(222,633)(223,632)(224,631)(225,630)(226,629)(227,628)(228,627)(229,626)(230,625)(231,624)(232,623)(233,622)(234,621)(235,620)(236,619)(237,618)(238,617)(239,616)(240,615)(241,614)(242,613)(243,612)(244,611)(245,610)(246,609)(247,608)(248,607)(249,606)(250,605)(251,604)(252,603)(253,602)(254,601)(255,600)(256,599)(257,598)(258,597)(259,596)(260,595)(261,594)(262,593)(263,592)(264,591)(265,590)(266,589)(267,588)(268,587)(269,586)(270,585)(271,584)(272,583)(273,582)(274,581)(275,580)(276,579)(277,578)(278,577)(279,576)(280,575)(281,574)(282,573)(283,572)(284,571)(285,570)(286,569)(287,568)(288,567)(289,566)(290,565)(291,564)(292,563)(293,562)(294,561)(295,560)(296,559)(297,558)(298,557)(299,556)(300,555)(301,554)(302,553)(303,552)(304,551)(305,550)(306,549)(307,548)(308,547)(309,546)(310,545)(311,544)(312,543)(313,542)(314,541)(315,540)(316,539)(317,538)(318,537)(319,536)(320,535)(321,534)(322,533)(323,532)(324,531)(325,530)(326,529)(327,528)(328,527)(329,526)(330,525)(331,524)(332,523)(333,522)(334,521)(335,520)(336,519)(337,518)(338,517)(339,516)(340,515)(341,514)(342,513)(343,512)(344,511)(345,510)(346,509)(347,508)(348,507)(349,506)(350,505)(351,504)(352,503)(353,502)(354,501)(355,500)(356,499)(357,498)(358,497)(359,496)(360,495)(361,494)(362,493)(363,492)(364,491)(365,490)(366,489)(367,488)(368,487)(369,486)(370,485)(371,484)(372,483)(373,482)(374,481)(375,480)(376,479)(377,478)(378,477)(379,476)(380,475)(381,474)(382,473)(383,472)(384,471)(385,470)(386,469)(387,468)(388,467)(389,466)(390,465)(391,464)(392,463)(393,462)(394,461)(395,460)(396,459)(397,458)(398,457)(399,456)(400,455)(401,454)(402,453)(403,452)(404,451)(405,450)(406,449)(407,448)(408,447)(409,446)(410,445)(411,444)(412,443)(413,442)(414,441)(415,440)(416,439)(417,438)(418,437)(419,436)(420,435)(421,434)(422,433)(423,432)(424,431)(425,430)(426,429)(427,428)Polycyclic presentation:
2,11,823,2|a^2=d,b^a=b^10,c^a=c^8229056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36212, 4);