Finite Group DatabasebetaFinite Group Databasebeta| order | 16288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C509 ⋊ #131 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 525 |
| transitive degree | μt(G) = 8144 |
A minimal faithful permutation representation — 3 generators on 525 points:
(1,2)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,87)(48,49)(51,83)(52,53)(55,79)(56,57)(59,75)(60,61)(63,71)(64,65)(66,67)(68,116)(69,70)(72,112)(73,74)(76,108)(77,78)(80,104)(81,82)(84,100)(85,86)(88,96)(89,90)(91,92)(93,149)(94,95)(97,145)(98,99)(101,141)(102,103)(105,137)(106,107)(109,133)(110,111)(113,129)(114,115)(117,125)(118,119)(120,121)(122,186)(123,124)(126,182)(127,128)(130,178)(131,132)(134,174)(135,136)(138,170)(139,140)(142,166)(143,144)(146,162)(147,148)(150,158)(151,152)(153,154)(155,227)(156,157)(159,223)(160,161)(163,219)(164,165)(167,215)(168,169)(171,211)(172,173)(175,207)(176,177)(179,203)(180,181)(183,199)(184,185)(187,195)(188,189)(190,191)(192,272)(193,194)(196,268)(197,198)(200,264)(201,202)(204,260)(205,206)(208,256)(209,210)(212,252)(213,214)(216,248)(217,218)(220,244)(221,222)(224,240)(225,226)(228,236)(229,230)(231,232)(233,321)(234,235)(237,317)(238,239)(241,313)(242,243)(245,309)(246,247)(249,305)(250,251)(253,301)(254,255)(257,297)(258,259)(261,293)(262,263)(265,289)(266,267)(269,285)(270,271)(273,281)(274,275)(276,277)(278,368)(279,280)(282,364)(283,284)(286,360)(287,288)(290,356)(291,292)(294,352)(295,296)(298,348)(299,300)(302,344)(303,304)(306,342)(307,308)(310,340)(311,312)(314,338)(315,316)(318,334)(319,320)(322,330)(323,324)(325,326)(327,341)(328,329)(331,339)(332,333)(336,337)(343,387)(345,383)(346,347)(349,379)(350,351)(353,378)(354,355)(357,377)(358,359)(361,376)(362,363)(365,375)(366,367)(369,374)(370,371)(372,373)(380,414)(381,382)(384,410)(385,386)(388,409)(389,390)(391,408)(392,393)(394,407)(395,396)(397,406)(398,399)(400,405)(401,402)(403,404)(411,437)(412,413)(415,436)(416,417)(418,435)(419,420)(421,434)(422,423)(424,433)(425,426)(427,432)(428,429)(430,431)(438,459)(439,440)(441,458)(442,443)(444,457)(445,446)(447,456)(448,449)(450,455)(451,452)(453,454)(460,477)(461,462)(463,476)(464,465)(466,475)(467,468)(469,474)(470,471)(472,473)(478,491)(479,480)(481,490)(482,483)(484,489)(485,486)(487,488)(492,501)(493,494)(495,500)(496,497)(498,499)(502,507)(503,504)(505,506)(508,509)(512,518)(515,521)(519,524)(522,525);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,64)(47,66)(49,69)(50,63)(51,62)(53,73)(54,59)(55,58)(57,77)(61,81)(65,85)(67,89)(68,91)(70,94)(71,88)(72,87)(74,98)(75,84)(76,83)(78,102)(79,80)(82,106)(86,110)(90,114)(92,118)(93,120)(95,123)(96,117)(97,116)(99,127)(100,113)(101,112)(103,131)(104,109)(105,108)(107,135)(111,139)(115,143)(119,147)(121,151)(122,153)(124,156)(125,150)(126,149)(128,160)(129,146)(130,145)(132,164)(133,142)(134,141)(136,168)(137,138)(140,172)(144,176)(148,180)(152,184)(154,188)(155,190)(157,193)(158,187)(159,186)(161,197)(162,183)(163,182)(165,201)(166,179)(167,178)(169,205)(170,175)(171,174)(173,209)(177,213)(181,217)(185,221)(189,225)(191,229)(192,231)(194,234)(195,228)(196,227)(198,238)(199,224)(200,223)(202,242)(203,220)(204,219)(206,246)(207,216)(208,215)(210,250)(211,212)(214,254)(218,258)(222,262)(226,266)(230,270)(232,274)(233,276)(235,279)(236,273)(237,272)(239,283)(240,269)(241,268)(243,287)(244,265)(245,264)(247,291)(248,261)(249,260)(251,295)(252,257)(253,256)(255,299)(259,303)(263,307)(267,311)(271,315)(275,319)(277,323)(278,325)(280,328)(281,322)(282,321)(284,332)(285,318)(286,317)(288,336)(289,314)(290,313)(292,337)(293,310)(294,309)(296,333)(297,306)(298,305)(300,329)(301,302)(304,346)(308,350)(312,354)(316,358)(320,362)(324,366)(326,370)(327,372)(330,369)(331,368)(334,365)(335,364)(338,361)(339,360)(340,357)(341,356)(342,353)(343,352)(344,349)(345,348)(347,381)(351,385)(355,389)(359,392)(363,395)(367,398)(371,401)(373,403)(374,382)(375,400)(376,397)(377,394)(378,391)(379,388)(380,387)(383,384)(386,412)(390,416)(393,419)(396,422)(399,425)(402,428)(404,430)(405,413)(406,427)(407,424)(408,421)(409,418)(410,415)(411,414)(417,439)(420,442)(423,445)(426,448)(429,451)(431,453)(432,440)(433,450)(434,447)(435,444)(436,441)(437,438)(443,461)(446,464)(449,467)(452,470)(454,472)(455,462)(456,469)(457,466)(458,463)(459,460)(465,479)(468,482)(471,485)(473,487)(474,480)(475,484)(476,481)(477,478)(483,493)(486,496)(488,498)(489,494)(490,495)(491,492)(497,503)(499,505)(500,504)(501,502)(506,509)(507,508)(510,512)(511,515)(513,519)(514,518)(516,522)(517,521)(520,524)(523,525);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,231)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,372)(284,331,332,368)(288,335,336,364)(292,339,337,360)(296,341,333,356)(300,343,329,352)(304,345,346,348)(308,349,350,344)(312,353,354,342)(316,357,358,340)(320,361,362,338)(324,365,366,334)(326,369,370,330)(347,380,381,387)(351,384,385,383)(355,388,389,379)(359,391,392,378)(363,394,395,377)(367,397,398,376)(371,400,401,375)(373,382,403,374)(386,411,412,414)(390,415,416,410)(393,418,419,409)(396,421,422,408)(399,424,425,407)(402,427,428,406)(404,413,430,405)(417,438,439,437)(420,441,442,436)(423,444,445,435)(426,447,448,434)(429,450,451,433)(431,440,453,432)(443,460,461,459)(446,463,464,458)(449,466,467,457)(452,469,470,456)(454,462,472,455)(465,478,479,477)(468,481,482,476)(471,484,485,475)(473,480,487,474)(483,492,493,491)(486,495,496,490)(488,494,498,489)(497,502,503,501)(499,504,505,500)(506,508,509,507)(510,511,513,516,514,517,520,523)(512,515,519,522,518,521,524,525)Polycyclic presentation:
2^5,509|a^2=d,d^2=e,f^a=f^301,c^b=ce,f^b=f^508,f^c=f^508,f^d=f^508655 conjugacy classes — view the full character table.
| maximal subgroup of | #45656281, #45656282, #45656283, … |
| maximal normal subgroup of | #45656281, #45656282, #45656283, … |
| maximal quotient of | #45656203, #45656213, #45656245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16288, 234);