Finite Group DatabasebetaFinite Group Databasebeta| order | 35036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8759 |
| unambiguous semidirect product | C19⋊Dic461 |
| derived, Hall | C19×C461 ⋊ C4 |
| Sylow | C461 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic461 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8759 |
| commutator, hypocenter | C19×C461 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C19×C461 | C2 |
| LCS | G ▷ C19×C461 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 484 |
| transitive degree | μt(G) = 35036 |
A minimal faithful permutation representation — 2 generators on 484 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);(1,3,2,4)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(25,484)(26,483)(27,482)(28,481)(29,480)(30,479)(31,478)(32,477)(33,476)(34,475)(35,474)(36,473)(37,472)(38,471)(39,470)(40,469)(41,468)(42,467)(43,466)(44,465)(45,464)(46,463)(47,462)(48,461)(49,460)(50,459)(51,458)(52,457)(53,456)(54,455)(55,454)(56,453)(57,452)(58,451)(59,450)(60,449)(61,448)(62,447)(63,446)(64,445)(65,444)(66,443)(67,442)(68,441)(69,440)(70,439)(71,438)(72,437)(73,436)(74,435)(75,434)(76,433)(77,432)(78,431)(79,430)(80,429)(81,428)(82,427)(83,426)(84,425)(85,424)(86,423)(87,422)(88,421)(89,420)(90,419)(91,418)(92,417)(93,416)(94,415)(95,414)(96,413)(97,412)(98,411)(99,410)(100,409)(101,408)(102,407)(103,406)(104,405)(105,404)(106,403)(107,402)(108,401)(109,400)(110,399)(111,398)(112,397)(113,396)(114,395)(115,394)(116,393)(117,392)(118,391)(119,390)(120,389)(121,388)(122,387)(123,386)(124,385)(125,384)(126,383)(127,382)(128,381)(129,380)(130,379)(131,378)(132,377)(133,376)(134,375)(135,374)(136,373)(137,372)(138,371)(139,370)(140,369)(141,368)(142,367)(143,366)(144,365)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)(160,349)(161,348)(162,347)(163,346)(164,345)(165,344)(166,343)(167,342)(168,341)(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)(176,333)(177,332)(178,331)(179,330)(180,329)(181,328)(182,327)(183,326)(184,325)(185,324)(186,323)(187,322)(188,321)(189,320)(190,319)(191,318)(192,317)(193,316)(194,315)(195,314)(196,313)(197,312)(198,311)(199,310)(200,309)(201,308)(202,307)(203,306)(204,305)(205,304)(206,303)(207,302)(208,301)(209,300)(210,299)(211,298)(212,297)(213,296)(214,295)(215,294)(216,293)(217,292)(218,291)(219,290)(220,289)(221,288)(222,287)(223,286)(224,285)(225,284)(226,283)(227,282)(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)(234,275)(235,274)(236,273)(237,272)(238,271)(239,270)(240,269)(241,268)(242,267)(243,266)(244,265)(245,264)(246,263)(247,262)(248,261)(249,260)(250,259)(251,258)(252,257)(253,256)(254,255)Polycyclic presentation:
2,19,461,2|a^2=d,b^a=b^18,c^a=c^4608762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35036, 4);