Finite Group DatabasebetaFinite Group Databasebeta| order | 36470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18235 |
| unambiguous semidirect product | C5⋊D3647 |
| unambiguous semidirect product | C7⋊D2605 |
| unambiguous semidirect product | C521⋊D35 |
| Fitting, socle, derived, Hall | C5×C7×C521 ⋊ C2 |
| Hall | C7×C521 ⋊ D5 |
| Hall | C5×C521 ⋊ D7 |
| Sylow | C521 ⋊ D35 |
| Hall | C5×C7 ⋊ D521 |
| Sylow | C7 ⋊ D2605 |
| Sylow | C5 ⋊ D3647 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C521 | C2 |
| LCS | G ▷ C5×C7×C521 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 533 |
| transitive degree | μt(G) = 18235 |
A minimal faithful permutation representation — 2 generators on 533 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);(2,5)(3,4)(7,12)(8,11)(9,10)(14,533)(15,532)(16,531)(17,530)(18,529)(19,528)(20,527)(21,526)(22,525)(23,524)(24,523)(25,522)(26,521)(27,520)(28,519)(29,518)(30,517)(31,516)(32,515)(33,514)(34,513)(35,512)(36,511)(37,510)(38,509)(39,508)(40,507)(41,506)(42,505)(43,504)(44,503)(45,502)(46,501)(47,500)(48,499)(49,498)(50,497)(51,496)(52,495)(53,494)(54,493)(55,492)(56,491)(57,490)(58,489)(59,488)(60,487)(61,486)(62,485)(63,484)(64,483)(65,482)(66,481)(67,480)(68,479)(69,478)(70,477)(71,476)(72,475)(73,474)(74,473)(75,472)(76,471)(77,470)(78,469)(79,468)(80,467)(81,466)(82,465)(83,464)(84,463)(85,462)(86,461)(87,460)(88,459)(89,458)(90,457)(91,456)(92,455)(93,454)(94,453)(95,452)(96,451)(97,450)(98,449)(99,448)(100,447)(101,446)(102,445)(103,444)(104,443)(105,442)(106,441)(107,440)(108,439)(109,438)(110,437)(111,436)(112,435)(113,434)(114,433)(115,432)(116,431)(117,430)(118,429)(119,428)(120,427)(121,426)(122,425)(123,424)(124,423)(125,422)(126,421)(127,420)(128,419)(129,418)(130,417)(131,416)(132,415)(133,414)(134,413)(135,412)(136,411)(137,410)(138,409)(139,408)(140,407)(141,406)(142,405)(143,404)(144,403)(145,402)(146,401)(147,400)(148,399)(149,398)(150,397)(151,396)(152,395)(153,394)(154,393)(155,392)(156,391)(157,390)(158,389)(159,388)(160,387)(161,386)(162,385)(163,384)(164,383)(165,382)(166,381)(167,380)(168,379)(169,378)(170,377)(171,376)(172,375)(173,374)(174,373)(175,372)(176,371)(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)(184,363)(185,362)(186,361)(187,360)(188,359)(189,358)(190,357)(191,356)(192,355)(193,354)(194,353)(195,352)(196,351)(197,350)(198,349)(199,348)(200,347)(201,346)(202,345)(203,344)(204,343)(205,342)(206,341)(207,340)(208,339)(209,338)(210,337)(211,336)(212,335)(213,334)(214,333)(215,332)(216,331)(217,330)(218,329)(219,328)(220,327)(221,326)(222,325)(223,324)(224,323)(225,322)(226,321)(227,320)(228,319)(229,318)(230,317)(231,316)(232,315)(233,314)(234,313)(235,312)(236,311)(237,310)(238,309)(239,308)(240,307)(241,306)(242,305)(243,304)(244,303)(245,302)(246,301)(247,300)(248,299)(249,298)(250,297)(251,296)(252,295)(253,294)(254,293)(255,292)(256,291)(257,290)(258,289)(259,288)(260,287)(261,286)(262,285)(263,284)(264,283)(265,282)(266,281)(267,280)(268,279)(269,278)(270,277)(271,276)(272,275)(273,274)Polycyclic presentation:
2,5,7,521|b^a=b^4,c^a=c^6,d^a=d^5209119 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36470, 9);