Finite Group DatabasebetaFinite Group Databasebeta| order | 33084 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8271 |
| unambiguous semidirect product | C9⋊Dic919 |
| unambiguous semidirect product | C919⋊Dic9 |
| derived, Hall | C9×C919 ⋊ C4 |
| Sylow | C919 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic919 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D8271 |
| commutator, hypocenter | C9×C919 | C4 |
| Frattini | C2×C3 | D2757 |
| Fitting, cosocle | C2×C9×C919 | C2 |
| socle, prime radical | C2×C3×C919 | D3 |
| LCS | G ▷ C9×C919 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 932 |
| transitive degree | μt(G) = 33084 |
A minimal faithful permutation representation — 2 generators on 932 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,932)(16,931)(17,930)(18,929)(19,928)(20,927)(21,926)(22,925)(23,924)(24,923)(25,922)(26,921)(27,920)(28,919)(29,918)(30,917)(31,916)(32,915)(33,914)(34,913)(35,912)(36,911)(37,910)(38,909)(39,908)(40,907)(41,906)(42,905)(43,904)(44,903)(45,902)(46,901)(47,900)(48,899)(49,898)(50,897)(51,896)(52,895)(53,894)(54,893)(55,892)(56,891)(57,890)(58,889)(59,888)(60,887)(61,886)(62,885)(63,884)(64,883)(65,882)(66,881)(67,880)(68,879)(69,878)(70,877)(71,876)(72,875)(73,874)(74,873)(75,872)(76,871)(77,870)(78,869)(79,868)(80,867)(81,866)(82,865)(83,864)(84,863)(85,862)(86,861)(87,860)(88,859)(89,858)(90,857)(91,856)(92,855)(93,854)(94,853)(95,852)(96,851)(97,850)(98,849)(99,848)(100,847)(101,846)(102,845)(103,844)(104,843)(105,842)(106,841)(107,840)(108,839)(109,838)(110,837)(111,836)(112,835)(113,834)(114,833)(115,832)(116,831)(117,830)(118,829)(119,828)(120,827)(121,826)(122,825)(123,824)(124,823)(125,822)(126,821)(127,820)(128,819)(129,818)(130,817)(131,816)(132,815)(133,814)(134,813)(135,812)(136,811)(137,810)(138,809)(139,808)(140,807)(141,806)(142,805)(143,804)(144,803)(145,802)(146,801)(147,800)(148,799)(149,798)(150,797)(151,796)(152,795)(153,794)(154,793)(155,792)(156,791)(157,790)(158,789)(159,788)(160,787)(161,786)(162,785)(163,784)(164,783)(165,782)(166,781)(167,780)(168,779)(169,778)(170,777)(171,776)(172,775)(173,774)(174,773)(175,772)(176,771)(177,770)(178,769)(179,768)(180,767)(181,766)(182,765)(183,764)(184,763)(185,762)(186,761)(187,760)(188,759)(189,758)(190,757)(191,756)(192,755)(193,754)(194,753)(195,752)(196,751)(197,750)(198,749)(199,748)(200,747)(201,746)(202,745)(203,744)(204,743)(205,742)(206,741)(207,740)(208,739)(209,738)(210,737)(211,736)(212,735)(213,734)(214,733)(215,732)(216,731)(217,730)(218,729)(219,728)(220,727)(221,726)(222,725)(223,724)(224,723)(225,722)(226,721)(227,720)(228,719)(229,718)(230,717)(231,716)(232,715)(233,714)(234,713)(235,712)(236,711)(237,710)(238,709)(239,708)(240,707)(241,706)(242,705)(243,704)(244,703)(245,702)(246,701)(247,700)(248,699)(249,698)(250,697)(251,696)(252,695)(253,694)(254,693)(255,692)(256,691)(257,690)(258,689)(259,688)(260,687)(261,686)(262,685)(263,684)(264,683)(265,682)(266,681)(267,680)(268,679)(269,678)(270,677)(271,676)(272,675)(273,674)(274,673)(275,672)(276,671)(277,670)(278,669)(279,668)(280,667)(281,666)(282,665)(283,664)(284,663)(285,662)(286,661)(287,660)(288,659)(289,658)(290,657)(291,656)(292,655)(293,654)(294,653)(295,652)(296,651)(297,650)(298,649)(299,648)(300,647)(301,646)(302,645)(303,644)(304,643)(305,642)(306,641)(307,640)(308,639)(309,638)(310,637)(311,636)(312,635)(313,634)(314,633)(315,632)(316,631)(317,630)(318,629)(319,628)(320,627)(321,626)(322,625)(323,624)(324,623)(325,622)(326,621)(327,620)(328,619)(329,618)(330,617)(331,616)(332,615)(333,614)(334,613)(335,612)(336,611)(337,610)(338,609)(339,608)(340,607)(341,606)(342,605)(343,604)(344,603)(345,602)(346,601)(347,600)(348,599)(349,598)(350,597)(351,596)(352,595)(353,594)(354,593)(355,592)(356,591)(357,590)(358,589)(359,588)(360,587)(361,586)(362,585)(363,584)(364,583)(365,582)(366,581)(367,580)(368,579)(369,578)(370,577)(371,576)(372,575)(373,574)(374,573)(375,572)(376,571)(377,570)(378,569)(379,568)(380,567)(381,566)(382,565)(383,564)(384,563)(385,562)(386,561)(387,560)(388,559)(389,558)(390,557)(391,556)(392,555)(393,554)(394,553)(395,552)(396,551)(397,550)(398,549)(399,548)(400,547)(401,546)(402,545)(403,544)(404,543)(405,542)(406,541)(407,540)(408,539)(409,538)(410,537)(411,536)(412,535)(413,534)(414,533)(415,532)(416,531)(417,530)(418,529)(419,528)(420,527)(421,526)(422,525)(423,524)(424,523)(425,522)(426,521)(427,520)(428,519)(429,518)(430,517)(431,516)(432,515)(433,514)(434,513)(435,512)(436,511)(437,510)(438,509)(439,508)(440,507)(441,506)(442,505)(443,504)(444,503)(445,502)(446,501)(447,500)(448,499)(449,498)(450,497)(451,496)(452,495)(453,494)(454,493)(455,492)(456,491)(457,490)(458,489)(459,488)(460,487)(461,486)(462,485)(463,484)(464,483)(465,482)(466,481)(467,480)(468,479)(469,478)(470,477)(471,476)(472,475)(473,474)Polycyclic presentation:
2,3,919,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^918,e^a=e^28274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33084, 6);