Finite Group DatabasebetaFinite Group Databasebeta| order | 37796 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9449 |
| unambiguous semidirect product | C11⋊Dic859 |
| unambiguous semidirect product | C859⋊Dic11 |
| derived, Hall | C11×C859 ⋊ C4 |
| Sylow | C859 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic859 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9449 |
| commutator, hypocenter | C11×C859 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C859 | C2 |
| LCS | G ▷ C11×C859 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 874 |
| transitive degree | μt(G) = 37796 |
A minimal faithful permutation representation — 2 generators on 874 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,874)(18,873)(19,872)(20,871)(21,870)(22,869)(23,868)(24,867)(25,866)(26,865)(27,864)(28,863)(29,862)(30,861)(31,860)(32,859)(33,858)(34,857)(35,856)(36,855)(37,854)(38,853)(39,852)(40,851)(41,850)(42,849)(43,848)(44,847)(45,846)(46,845)(47,844)(48,843)(49,842)(50,841)(51,840)(52,839)(53,838)(54,837)(55,836)(56,835)(57,834)(58,833)(59,832)(60,831)(61,830)(62,829)(63,828)(64,827)(65,826)(66,825)(67,824)(68,823)(69,822)(70,821)(71,820)(72,819)(73,818)(74,817)(75,816)(76,815)(77,814)(78,813)(79,812)(80,811)(81,810)(82,809)(83,808)(84,807)(85,806)(86,805)(87,804)(88,803)(89,802)(90,801)(91,800)(92,799)(93,798)(94,797)(95,796)(96,795)(97,794)(98,793)(99,792)(100,791)(101,790)(102,789)(103,788)(104,787)(105,786)(106,785)(107,784)(108,783)(109,782)(110,781)(111,780)(112,779)(113,778)(114,777)(115,776)(116,775)(117,774)(118,773)(119,772)(120,771)(121,770)(122,769)(123,768)(124,767)(125,766)(126,765)(127,764)(128,763)(129,762)(130,761)(131,760)(132,759)(133,758)(134,757)(135,756)(136,755)(137,754)(138,753)(139,752)(140,751)(141,750)(142,749)(143,748)(144,747)(145,746)(146,745)(147,744)(148,743)(149,742)(150,741)(151,740)(152,739)(153,738)(154,737)(155,736)(156,735)(157,734)(158,733)(159,732)(160,731)(161,730)(162,729)(163,728)(164,727)(165,726)(166,725)(167,724)(168,723)(169,722)(170,721)(171,720)(172,719)(173,718)(174,717)(175,716)(176,715)(177,714)(178,713)(179,712)(180,711)(181,710)(182,709)(183,708)(184,707)(185,706)(186,705)(187,704)(188,703)(189,702)(190,701)(191,700)(192,699)(193,698)(194,697)(195,696)(196,695)(197,694)(198,693)(199,692)(200,691)(201,690)(202,689)(203,688)(204,687)(205,686)(206,685)(207,684)(208,683)(209,682)(210,681)(211,680)(212,679)(213,678)(214,677)(215,676)(216,675)(217,674)(218,673)(219,672)(220,671)(221,670)(222,669)(223,668)(224,667)(225,666)(226,665)(227,664)(228,663)(229,662)(230,661)(231,660)(232,659)(233,658)(234,657)(235,656)(236,655)(237,654)(238,653)(239,652)(240,651)(241,650)(242,649)(243,648)(244,647)(245,646)(246,645)(247,644)(248,643)(249,642)(250,641)(251,640)(252,639)(253,638)(254,637)(255,636)(256,635)(257,634)(258,633)(259,632)(260,631)(261,630)(262,629)(263,628)(264,627)(265,626)(266,625)(267,624)(268,623)(269,622)(270,621)(271,620)(272,619)(273,618)(274,617)(275,616)(276,615)(277,614)(278,613)(279,612)(280,611)(281,610)(282,609)(283,608)(284,607)(285,606)(286,605)(287,604)(288,603)(289,602)(290,601)(291,600)(292,599)(293,598)(294,597)(295,596)(296,595)(297,594)(298,593)(299,592)(300,591)(301,590)(302,589)(303,588)(304,587)(305,586)(306,585)(307,584)(308,583)(309,582)(310,581)(311,580)(312,579)(313,578)(314,577)(315,576)(316,575)(317,574)(318,573)(319,572)(320,571)(321,570)(322,569)(323,568)(324,567)(325,566)(326,565)(327,564)(328,563)(329,562)(330,561)(331,560)(332,559)(333,558)(334,557)(335,556)(336,555)(337,554)(338,553)(339,552)(340,551)(341,550)(342,549)(343,548)(344,547)(345,546)(346,545)(347,544)(348,543)(349,542)(350,541)(351,540)(352,539)(353,538)(354,537)(355,536)(356,535)(357,534)(358,533)(359,532)(360,531)(361,530)(362,529)(363,528)(364,527)(365,526)(366,525)(367,524)(368,523)(369,522)(370,521)(371,520)(372,519)(373,518)(374,517)(375,516)(376,515)(377,514)(378,513)(379,512)(380,511)(381,510)(382,509)(383,508)(384,507)(385,506)(386,505)(387,504)(388,503)(389,502)(390,501)(391,500)(392,499)(393,498)(394,497)(395,496)(396,495)(397,494)(398,493)(399,492)(400,491)(401,490)(402,489)(403,488)(404,487)(405,486)(406,485)(407,484)(408,483)(409,482)(410,481)(411,480)(412,479)(413,478)(414,477)(415,476)(416,475)(417,474)(418,473)(419,472)(420,471)(421,470)(422,469)(423,468)(424,467)(425,466)(426,465)(427,464)(428,463)(429,462)(430,461)(431,460)(432,459)(433,458)(434,457)(435,456)(436,455)(437,454)(438,453)(439,452)(440,451)(441,450)(442,449)(443,448)(444,447)(445,446)Polycyclic presentation:
2,11,859,2|a^2=d,b^a=b^10,c^a=c^8589452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37796, 6);