Finite Group DatabasebetaFinite Group Databasebeta| order | 36916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9229 |
| unambiguous semidirect product | C11⋊Dic839 |
| unambiguous semidirect product | C839⋊Dic11 |
| derived, Hall | C11×C839 ⋊ C4 |
| Sylow | C839 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic839 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9229 |
| commutator, hypocenter | C11×C839 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C839 | C2 |
| LCS | G ▷ C11×C839 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 854 |
| transitive degree | μt(G) = 36916 |
A minimal faithful permutation representation — 2 generators on 854 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,854)(18,853)(19,852)(20,851)(21,850)(22,849)(23,848)(24,847)(25,846)(26,845)(27,844)(28,843)(29,842)(30,841)(31,840)(32,839)(33,838)(34,837)(35,836)(36,835)(37,834)(38,833)(39,832)(40,831)(41,830)(42,829)(43,828)(44,827)(45,826)(46,825)(47,824)(48,823)(49,822)(50,821)(51,820)(52,819)(53,818)(54,817)(55,816)(56,815)(57,814)(58,813)(59,812)(60,811)(61,810)(62,809)(63,808)(64,807)(65,806)(66,805)(67,804)(68,803)(69,802)(70,801)(71,800)(72,799)(73,798)(74,797)(75,796)(76,795)(77,794)(78,793)(79,792)(80,791)(81,790)(82,789)(83,788)(84,787)(85,786)(86,785)(87,784)(88,783)(89,782)(90,781)(91,780)(92,779)(93,778)(94,777)(95,776)(96,775)(97,774)(98,773)(99,772)(100,771)(101,770)(102,769)(103,768)(104,767)(105,766)(106,765)(107,764)(108,763)(109,762)(110,761)(111,760)(112,759)(113,758)(114,757)(115,756)(116,755)(117,754)(118,753)(119,752)(120,751)(121,750)(122,749)(123,748)(124,747)(125,746)(126,745)(127,744)(128,743)(129,742)(130,741)(131,740)(132,739)(133,738)(134,737)(135,736)(136,735)(137,734)(138,733)(139,732)(140,731)(141,730)(142,729)(143,728)(144,727)(145,726)(146,725)(147,724)(148,723)(149,722)(150,721)(151,720)(152,719)(153,718)(154,717)(155,716)(156,715)(157,714)(158,713)(159,712)(160,711)(161,710)(162,709)(163,708)(164,707)(165,706)(166,705)(167,704)(168,703)(169,702)(170,701)(171,700)(172,699)(173,698)(174,697)(175,696)(176,695)(177,694)(178,693)(179,692)(180,691)(181,690)(182,689)(183,688)(184,687)(185,686)(186,685)(187,684)(188,683)(189,682)(190,681)(191,680)(192,679)(193,678)(194,677)(195,676)(196,675)(197,674)(198,673)(199,672)(200,671)(201,670)(202,669)(203,668)(204,667)(205,666)(206,665)(207,664)(208,663)(209,662)(210,661)(211,660)(212,659)(213,658)(214,657)(215,656)(216,655)(217,654)(218,653)(219,652)(220,651)(221,650)(222,649)(223,648)(224,647)(225,646)(226,645)(227,644)(228,643)(229,642)(230,641)(231,640)(232,639)(233,638)(234,637)(235,636)(236,635)(237,634)(238,633)(239,632)(240,631)(241,630)(242,629)(243,628)(244,627)(245,626)(246,625)(247,624)(248,623)(249,622)(250,621)(251,620)(252,619)(253,618)(254,617)(255,616)(256,615)(257,614)(258,613)(259,612)(260,611)(261,610)(262,609)(263,608)(264,607)(265,606)(266,605)(267,604)(268,603)(269,602)(270,601)(271,600)(272,599)(273,598)(274,597)(275,596)(276,595)(277,594)(278,593)(279,592)(280,591)(281,590)(282,589)(283,588)(284,587)(285,586)(286,585)(287,584)(288,583)(289,582)(290,581)(291,580)(292,579)(293,578)(294,577)(295,576)(296,575)(297,574)(298,573)(299,572)(300,571)(301,570)(302,569)(303,568)(304,567)(305,566)(306,565)(307,564)(308,563)(309,562)(310,561)(311,560)(312,559)(313,558)(314,557)(315,556)(316,555)(317,554)(318,553)(319,552)(320,551)(321,550)(322,549)(323,548)(324,547)(325,546)(326,545)(327,544)(328,543)(329,542)(330,541)(331,540)(332,539)(333,538)(334,537)(335,536)(336,535)(337,534)(338,533)(339,532)(340,531)(341,530)(342,529)(343,528)(344,527)(345,526)(346,525)(347,524)(348,523)(349,522)(350,521)(351,520)(352,519)(353,518)(354,517)(355,516)(356,515)(357,514)(358,513)(359,512)(360,511)(361,510)(362,509)(363,508)(364,507)(365,506)(366,505)(367,504)(368,503)(369,502)(370,501)(371,500)(372,499)(373,498)(374,497)(375,496)(376,495)(377,494)(378,493)(379,492)(380,491)(381,490)(382,489)(383,488)(384,487)(385,486)(386,485)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)(404,467)(405,466)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(435,436)Polycyclic presentation:
2,11,839,2|a^2=d,b^a=b^10,c^a=c^8389232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36916, 4);