Finite Group DatabasebetaFinite Group Databasebeta| order | 20098 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10049 |
| unambiguous semidirect product | C13⋊D773 |
| unambiguous semidirect product | C773⋊D13 |
| Fitting, socle, derived, Hall | C13×C773 ⋊ C2 |
| Sylow | C773 ⋊ D13 |
| Sylow | C13 ⋊ D773 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C773 | C2 |
| LCS | G ▷ C13×C773 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 786 |
| transitive degree | μt(G) = 10049 |
A minimal faithful permutation representation — 2 generators on 786 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,786)(16,785)(17,784)(18,783)(19,782)(20,781)(21,780)(22,779)(23,778)(24,777)(25,776)(26,775)(27,774)(28,773)(29,772)(30,771)(31,770)(32,769)(33,768)(34,767)(35,766)(36,765)(37,764)(38,763)(39,762)(40,761)(41,760)(42,759)(43,758)(44,757)(45,756)(46,755)(47,754)(48,753)(49,752)(50,751)(51,750)(52,749)(53,748)(54,747)(55,746)(56,745)(57,744)(58,743)(59,742)(60,741)(61,740)(62,739)(63,738)(64,737)(65,736)(66,735)(67,734)(68,733)(69,732)(70,731)(71,730)(72,729)(73,728)(74,727)(75,726)(76,725)(77,724)(78,723)(79,722)(80,721)(81,720)(82,719)(83,718)(84,717)(85,716)(86,715)(87,714)(88,713)(89,712)(90,711)(91,710)(92,709)(93,708)(94,707)(95,706)(96,705)(97,704)(98,703)(99,702)(100,701)(101,700)(102,699)(103,698)(104,697)(105,696)(106,695)(107,694)(108,693)(109,692)(110,691)(111,690)(112,689)(113,688)(114,687)(115,686)(116,685)(117,684)(118,683)(119,682)(120,681)(121,680)(122,679)(123,678)(124,677)(125,676)(126,675)(127,674)(128,673)(129,672)(130,671)(131,670)(132,669)(133,668)(134,667)(135,666)(136,665)(137,664)(138,663)(139,662)(140,661)(141,660)(142,659)(143,658)(144,657)(145,656)(146,655)(147,654)(148,653)(149,652)(150,651)(151,650)(152,649)(153,648)(154,647)(155,646)(156,645)(157,644)(158,643)(159,642)(160,641)(161,640)(162,639)(163,638)(164,637)(165,636)(166,635)(167,634)(168,633)(169,632)(170,631)(171,630)(172,629)(173,628)(174,627)(175,626)(176,625)(177,624)(178,623)(179,622)(180,621)(181,620)(182,619)(183,618)(184,617)(185,616)(186,615)(187,614)(188,613)(189,612)(190,611)(191,610)(192,609)(193,608)(194,607)(195,606)(196,605)(197,604)(198,603)(199,602)(200,601)(201,600)(202,599)(203,598)(204,597)(205,596)(206,595)(207,594)(208,593)(209,592)(210,591)(211,590)(212,589)(213,588)(214,587)(215,586)(216,585)(217,584)(218,583)(219,582)(220,581)(221,580)(222,579)(223,578)(224,577)(225,576)(226,575)(227,574)(228,573)(229,572)(230,571)(231,570)(232,569)(233,568)(234,567)(235,566)(236,565)(237,564)(238,563)(239,562)(240,561)(241,560)(242,559)(243,558)(244,557)(245,556)(246,555)(247,554)(248,553)(249,552)(250,551)(251,550)(252,549)(253,548)(254,547)(255,546)(256,545)(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)(264,537)(265,536)(266,535)(267,534)(268,533)(269,532)(270,531)(271,530)(272,529)(273,528)(274,527)(275,526)(276,525)(277,524)(278,523)(279,522)(280,521)(281,520)(282,519)(283,518)(284,517)(285,516)(286,515)(287,514)(288,513)(289,512)(290,511)(291,510)(292,509)(293,508)(294,507)(295,506)(296,505)(297,504)(298,503)(299,502)(300,501)(301,500)(302,499)(303,498)(304,497)(305,496)(306,495)(307,494)(308,493)(309,492)(310,491)(311,490)(312,489)(313,488)(314,487)(315,486)(316,485)(317,484)(318,483)(319,482)(320,481)(321,480)(322,479)(323,478)(324,477)(325,476)(326,475)(327,474)(328,473)(329,472)(330,471)(331,470)(332,469)(333,468)(334,467)(335,466)(336,465)(337,464)(338,463)(339,462)(340,461)(341,460)(342,459)(343,458)(344,457)(345,456)(346,455)(347,454)(348,453)(349,452)(350,451)(351,450)(352,449)(353,448)(354,447)(355,446)(356,445)(357,444)(358,443)(359,442)(360,441)(361,440)(362,439)(363,438)(364,437)(365,436)(366,435)(367,434)(368,433)(369,432)(370,431)(371,430)(372,429)(373,428)(374,427)(375,426)(376,425)(377,424)(378,423)(379,422)(380,421)(381,420)(382,419)(383,418)(384,417)(385,416)(386,415)(387,414)(388,413)(389,412)(390,411)(391,410)(392,409)(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401)Polycyclic presentation:
2,13,773|b^a=b^12,c^a=c^7725026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20098, 3);