Finite Group DatabasebetaFinite Group Databasebeta| order | 33706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16853 |
| unambiguous semidirect product | C19⋊D887 |
| unambiguous semidirect product | C887⋊D19 |
| Fitting, socle, derived, Hall | C19×C887 ⋊ C2 |
| Sylow | C887 ⋊ D19 |
| Sylow | C19 ⋊ D887 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C887 | C2 |
| LCS | G ▷ C19×C887 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 906 |
| transitive degree | μt(G) = 16853 |
A minimal faithful permutation representation — 2 generators on 906 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);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,906)(22,905)(23,904)(24,903)(25,902)(26,901)(27,900)(28,899)(29,898)(30,897)(31,896)(32,895)(33,894)(34,893)(35,892)(36,891)(37,890)(38,889)(39,888)(40,887)(41,886)(42,885)(43,884)(44,883)(45,882)(46,881)(47,880)(48,879)(49,878)(50,877)(51,876)(52,875)(53,874)(54,873)(55,872)(56,871)(57,870)(58,869)(59,868)(60,867)(61,866)(62,865)(63,864)(64,863)(65,862)(66,861)(67,860)(68,859)(69,858)(70,857)(71,856)(72,855)(73,854)(74,853)(75,852)(76,851)(77,850)(78,849)(79,848)(80,847)(81,846)(82,845)(83,844)(84,843)(85,842)(86,841)(87,840)(88,839)(89,838)(90,837)(91,836)(92,835)(93,834)(94,833)(95,832)(96,831)(97,830)(98,829)(99,828)(100,827)(101,826)(102,825)(103,824)(104,823)(105,822)(106,821)(107,820)(108,819)(109,818)(110,817)(111,816)(112,815)(113,814)(114,813)(115,812)(116,811)(117,810)(118,809)(119,808)(120,807)(121,806)(122,805)(123,804)(124,803)(125,802)(126,801)(127,800)(128,799)(129,798)(130,797)(131,796)(132,795)(133,794)(134,793)(135,792)(136,791)(137,790)(138,789)(139,788)(140,787)(141,786)(142,785)(143,784)(144,783)(145,782)(146,781)(147,780)(148,779)(149,778)(150,777)(151,776)(152,775)(153,774)(154,773)(155,772)(156,771)(157,770)(158,769)(159,768)(160,767)(161,766)(162,765)(163,764)(164,763)(165,762)(166,761)(167,760)(168,759)(169,758)(170,757)(171,756)(172,755)(173,754)(174,753)(175,752)(176,751)(177,750)(178,749)(179,748)(180,747)(181,746)(182,745)(183,744)(184,743)(185,742)(186,741)(187,740)(188,739)(189,738)(190,737)(191,736)(192,735)(193,734)(194,733)(195,732)(196,731)(197,730)(198,729)(199,728)(200,727)(201,726)(202,725)(203,724)(204,723)(205,722)(206,721)(207,720)(208,719)(209,718)(210,717)(211,716)(212,715)(213,714)(214,713)(215,712)(216,711)(217,710)(218,709)(219,708)(220,707)(221,706)(222,705)(223,704)(224,703)(225,702)(226,701)(227,700)(228,699)(229,698)(230,697)(231,696)(232,695)(233,694)(234,693)(235,692)(236,691)(237,690)(238,689)(239,688)(240,687)(241,686)(242,685)(243,684)(244,683)(245,682)(246,681)(247,680)(248,679)(249,678)(250,677)(251,676)(252,675)(253,674)(254,673)(255,672)(256,671)(257,670)(258,669)(259,668)(260,667)(261,666)(262,665)(263,664)(264,663)(265,662)(266,661)(267,660)(268,659)(269,658)(270,657)(271,656)(272,655)(273,654)(274,653)(275,652)(276,651)(277,650)(278,649)(279,648)(280,647)(281,646)(282,645)(283,644)(284,643)(285,642)(286,641)(287,640)(288,639)(289,638)(290,637)(291,636)(292,635)(293,634)(294,633)(295,632)(296,631)(297,630)(298,629)(299,628)(300,627)(301,626)(302,625)(303,624)(304,623)(305,622)(306,621)(307,620)(308,619)(309,618)(310,617)(311,616)(312,615)(313,614)(314,613)(315,612)(316,611)(317,610)(318,609)(319,608)(320,607)(321,606)(322,605)(323,604)(324,603)(325,602)(326,601)(327,600)(328,599)(329,598)(330,597)(331,596)(332,595)(333,594)(334,593)(335,592)(336,591)(337,590)(338,589)(339,588)(340,587)(341,586)(342,585)(343,584)(344,583)(345,582)(346,581)(347,580)(348,579)(349,578)(350,577)(351,576)(352,575)(353,574)(354,573)(355,572)(356,571)(357,570)(358,569)(359,568)(360,567)(361,566)(362,565)(363,564)(364,563)(365,562)(366,561)(367,560)(368,559)(369,558)(370,557)(371,556)(372,555)(373,554)(374,553)(375,552)(376,551)(377,550)(378,549)(379,548)(380,547)(381,546)(382,545)(383,544)(384,543)(385,542)(386,541)(387,540)(388,539)(389,538)(390,537)(391,536)(392,535)(393,534)(394,533)(395,532)(396,531)(397,530)(398,529)(399,528)(400,527)(401,526)(402,525)(403,524)(404,523)(405,522)(406,521)(407,520)(408,519)(409,518)(410,517)(411,516)(412,515)(413,514)(414,513)(415,512)(416,511)(417,510)(418,509)(419,508)(420,507)(421,506)(422,505)(423,504)(424,503)(425,502)(426,501)(427,500)(428,499)(429,498)(430,497)(431,496)(432,495)(433,494)(434,493)(435,492)(436,491)(437,490)(438,489)(439,488)(440,487)(441,486)(442,485)(443,484)(444,483)(445,482)(446,481)(447,480)(448,479)(449,478)(450,477)(451,476)(452,475)(453,474)(454,473)(455,472)(456,471)(457,470)(458,469)(459,468)(460,467)(461,466)(462,465)(463,464)Polycyclic presentation:
2,19,887|b^a=b^18,c^a=c^8868428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33706, 3);