Finite Group DatabasebetaFinite Group Databasebeta| order | 33732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8433 |
| unambiguous semidirect product | C9⋊Dic937 |
| derived, Hall | C9×C937 ⋊ C4 |
| Sylow | C937 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic937 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D8433 |
| commutator, hypocenter | C9×C937 | C4 |
| Frattini | C2×C3 | D2811 |
| Fitting, cosocle | C2×C9×C937 | C2 |
| socle, prime radical | C2×C3×C937 | D3 |
| LCS | G ▷ C9×C937 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 950 |
| transitive degree | μt(G) = 33732 |
A minimal faithful permutation representation — 2 generators on 950 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,950)(16,949)(17,948)(18,947)(19,946)(20,945)(21,944)(22,943)(23,942)(24,941)(25,940)(26,939)(27,938)(28,937)(29,936)(30,935)(31,934)(32,933)(33,932)(34,931)(35,930)(36,929)(37,928)(38,927)(39,926)(40,925)(41,924)(42,923)(43,922)(44,921)(45,920)(46,919)(47,918)(48,917)(49,916)(50,915)(51,914)(52,913)(53,912)(54,911)(55,910)(56,909)(57,908)(58,907)(59,906)(60,905)(61,904)(62,903)(63,902)(64,901)(65,900)(66,899)(67,898)(68,897)(69,896)(70,895)(71,894)(72,893)(73,892)(74,891)(75,890)(76,889)(77,888)(78,887)(79,886)(80,885)(81,884)(82,883)(83,882)(84,881)(85,880)(86,879)(87,878)(88,877)(89,876)(90,875)(91,874)(92,873)(93,872)(94,871)(95,870)(96,869)(97,868)(98,867)(99,866)(100,865)(101,864)(102,863)(103,862)(104,861)(105,860)(106,859)(107,858)(108,857)(109,856)(110,855)(111,854)(112,853)(113,852)(114,851)(115,850)(116,849)(117,848)(118,847)(119,846)(120,845)(121,844)(122,843)(123,842)(124,841)(125,840)(126,839)(127,838)(128,837)(129,836)(130,835)(131,834)(132,833)(133,832)(134,831)(135,830)(136,829)(137,828)(138,827)(139,826)(140,825)(141,824)(142,823)(143,822)(144,821)(145,820)(146,819)(147,818)(148,817)(149,816)(150,815)(151,814)(152,813)(153,812)(154,811)(155,810)(156,809)(157,808)(158,807)(159,806)(160,805)(161,804)(162,803)(163,802)(164,801)(165,800)(166,799)(167,798)(168,797)(169,796)(170,795)(171,794)(172,793)(173,792)(174,791)(175,790)(176,789)(177,788)(178,787)(179,786)(180,785)(181,784)(182,783)(183,782)(184,781)(185,780)(186,779)(187,778)(188,777)(189,776)(190,775)(191,774)(192,773)(193,772)(194,771)(195,770)(196,769)(197,768)(198,767)(199,766)(200,765)(201,764)(202,763)(203,762)(204,761)(205,760)(206,759)(207,758)(208,757)(209,756)(210,755)(211,754)(212,753)(213,752)(214,751)(215,750)(216,749)(217,748)(218,747)(219,746)(220,745)(221,744)(222,743)(223,742)(224,741)(225,740)(226,739)(227,738)(228,737)(229,736)(230,735)(231,734)(232,733)(233,732)(234,731)(235,730)(236,729)(237,728)(238,727)(239,726)(240,725)(241,724)(242,723)(243,722)(244,721)(245,720)(246,719)(247,718)(248,717)(249,716)(250,715)(251,714)(252,713)(253,712)(254,711)(255,710)(256,709)(257,708)(258,707)(259,706)(260,705)(261,704)(262,703)(263,702)(264,701)(265,700)(266,699)(267,698)(268,697)(269,696)(270,695)(271,694)(272,693)(273,692)(274,691)(275,690)(276,689)(277,688)(278,687)(279,686)(280,685)(281,684)(282,683)(283,682)(284,681)(285,680)(286,679)(287,678)(288,677)(289,676)(290,675)(291,674)(292,673)(293,672)(294,671)(295,670)(296,669)(297,668)(298,667)(299,666)(300,665)(301,664)(302,663)(303,662)(304,661)(305,660)(306,659)(307,658)(308,657)(309,656)(310,655)(311,654)(312,653)(313,652)(314,651)(315,650)(316,649)(317,648)(318,647)(319,646)(320,645)(321,644)(322,643)(323,642)(324,641)(325,640)(326,639)(327,638)(328,637)(329,636)(330,635)(331,634)(332,633)(333,632)(334,631)(335,630)(336,629)(337,628)(338,627)(339,626)(340,625)(341,624)(342,623)(343,622)(344,621)(345,620)(346,619)(347,618)(348,617)(349,616)(350,615)(351,614)(352,613)(353,612)(354,611)(355,610)(356,609)(357,608)(358,607)(359,606)(360,605)(361,604)(362,603)(363,602)(364,601)(365,600)(366,599)(367,598)(368,597)(369,596)(370,595)(371,594)(372,593)(373,592)(374,591)(375,590)(376,589)(377,588)(378,587)(379,586)(380,585)(381,584)(382,583)(383,582)(384,581)(385,580)(386,579)(387,578)(388,577)(389,576)(390,575)(391,574)(392,573)(393,572)(394,571)(395,570)(396,569)(397,568)(398,567)(399,566)(400,565)(401,564)(402,563)(403,562)(404,561)(405,560)(406,559)(407,558)(408,557)(409,556)(410,555)(411,554)(412,553)(413,552)(414,551)(415,550)(416,549)(417,548)(418,547)(419,546)(420,545)(421,544)(422,543)(423,542)(424,541)(425,540)(426,539)(427,538)(428,537)(429,536)(430,535)(431,534)(432,533)(433,532)(434,531)(435,530)(436,529)(437,528)(438,527)(439,526)(440,525)(441,524)(442,523)(443,522)(444,521)(445,520)(446,519)(447,518)(448,517)(449,516)(450,515)(451,514)(452,513)(453,512)(454,511)(455,510)(456,509)(457,508)(458,507)(459,506)(460,505)(461,504)(462,503)(463,502)(464,501)(465,500)(466,499)(467,498)(468,497)(469,496)(470,495)(471,494)(472,493)(473,492)(474,491)(475,490)(476,489)(477,488)(478,487)(479,486)(480,485)(481,484)(482,483)Polycyclic presentation:
2,3,937,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^936,e^a=e^28436 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33732, 6);