Finite Group DatabasebetaFinite Group Databasebeta| order | 23910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11955 |
| unambiguous semidirect product | C3⋊D3985 |
| unambiguous semidirect product | C5⋊D2391 |
| unambiguous semidirect product | C797⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C797 ⋊ C2 |
| Hall | C5×C797 ⋊ D3 |
| Hall | C3×C797 ⋊ D5 |
| Sylow | C797 ⋊ D15 |
| Hall | C3×C5 ⋊ D797 |
| Sylow | C5 ⋊ D2391 |
| Sylow | C3 ⋊ D3985 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C797 | C2 |
| LCS | G ▷ C3×C5×C797 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 805 |
| transitive degree | μt(G) = 11955 |
A minimal faithful permutation representation — 2 generators on 805 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);(2,3)(5,8)(6,7)(10,805)(11,804)(12,803)(13,802)(14,801)(15,800)(16,799)(17,798)(18,797)(19,796)(20,795)(21,794)(22,793)(23,792)(24,791)(25,790)(26,789)(27,788)(28,787)(29,786)(30,785)(31,784)(32,783)(33,782)(34,781)(35,780)(36,779)(37,778)(38,777)(39,776)(40,775)(41,774)(42,773)(43,772)(44,771)(45,770)(46,769)(47,768)(48,767)(49,766)(50,765)(51,764)(52,763)(53,762)(54,761)(55,760)(56,759)(57,758)(58,757)(59,756)(60,755)(61,754)(62,753)(63,752)(64,751)(65,750)(66,749)(67,748)(68,747)(69,746)(70,745)(71,744)(72,743)(73,742)(74,741)(75,740)(76,739)(77,738)(78,737)(79,736)(80,735)(81,734)(82,733)(83,732)(84,731)(85,730)(86,729)(87,728)(88,727)(89,726)(90,725)(91,724)(92,723)(93,722)(94,721)(95,720)(96,719)(97,718)(98,717)(99,716)(100,715)(101,714)(102,713)(103,712)(104,711)(105,710)(106,709)(107,708)(108,707)(109,706)(110,705)(111,704)(112,703)(113,702)(114,701)(115,700)(116,699)(117,698)(118,697)(119,696)(120,695)(121,694)(122,693)(123,692)(124,691)(125,690)(126,689)(127,688)(128,687)(129,686)(130,685)(131,684)(132,683)(133,682)(134,681)(135,680)(136,679)(137,678)(138,677)(139,676)(140,675)(141,674)(142,673)(143,672)(144,671)(145,670)(146,669)(147,668)(148,667)(149,666)(150,665)(151,664)(152,663)(153,662)(154,661)(155,660)(156,659)(157,658)(158,657)(159,656)(160,655)(161,654)(162,653)(163,652)(164,651)(165,650)(166,649)(167,648)(168,647)(169,646)(170,645)(171,644)(172,643)(173,642)(174,641)(175,640)(176,639)(177,638)(178,637)(179,636)(180,635)(181,634)(182,633)(183,632)(184,631)(185,630)(186,629)(187,628)(188,627)(189,626)(190,625)(191,624)(192,623)(193,622)(194,621)(195,620)(196,619)(197,618)(198,617)(199,616)(200,615)(201,614)(202,613)(203,612)(204,611)(205,610)(206,609)(207,608)(208,607)(209,606)(210,605)(211,604)(212,603)(213,602)(214,601)(215,600)(216,599)(217,598)(218,597)(219,596)(220,595)(221,594)(222,593)(223,592)(224,591)(225,590)(226,589)(227,588)(228,587)(229,586)(230,585)(231,584)(232,583)(233,582)(234,581)(235,580)(236,579)(237,578)(238,577)(239,576)(240,575)(241,574)(242,573)(243,572)(244,571)(245,570)(246,569)(247,568)(248,567)(249,566)(250,565)(251,564)(252,563)(253,562)(254,561)(255,560)(256,559)(257,558)(258,557)(259,556)(260,555)(261,554)(262,553)(263,552)(264,551)(265,550)(266,549)(267,548)(268,547)(269,546)(270,545)(271,544)(272,543)(273,542)(274,541)(275,540)(276,539)(277,538)(278,537)(279,536)(280,535)(281,534)(282,533)(283,532)(284,531)(285,530)(286,529)(287,528)(288,527)(289,526)(290,525)(291,524)(292,523)(293,522)(294,521)(295,520)(296,519)(297,518)(298,517)(299,516)(300,515)(301,514)(302,513)(303,512)(304,511)(305,510)(306,509)(307,508)(308,507)(309,506)(310,505)(311,504)(312,503)(313,502)(314,501)(315,500)(316,499)(317,498)(318,497)(319,496)(320,495)(321,494)(322,493)(323,492)(324,491)(325,490)(326,489)(327,488)(328,487)(329,486)(330,485)(331,484)(332,483)(333,482)(334,481)(335,480)(336,479)(337,478)(338,477)(339,476)(340,475)(341,474)(342,473)(343,472)(344,471)(345,470)(346,469)(347,468)(348,467)(349,466)(350,465)(351,464)(352,463)(353,462)(354,461)(355,460)(356,459)(357,458)(358,457)(359,456)(360,455)(361,454)(362,453)(363,452)(364,451)(365,450)(366,449)(367,448)(368,447)(369,446)(370,445)(371,444)(372,443)(373,442)(374,441)(375,440)(376,439)(377,438)(378,437)(379,436)(380,435)(381,434)(382,433)(383,432)(384,431)(385,430)(386,429)(387,428)(388,427)(389,426)(390,425)(391,424)(392,423)(393,422)(394,421)(395,420)(396,419)(397,418)(398,417)(399,416)(400,415)(401,414)(402,413)(403,412)(404,411)(405,410)(406,409)(407,408)Polycyclic presentation:
2,3,5,797|b^a=b^2,c^a=c^4,d^a=d^7965979 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23910, 8);