Finite Group DatabasebetaFinite Group Databasebeta| order | 38090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D19045 |
| unambiguous semidirect product | C5⋊D3809 |
| unambiguous semidirect product | C13⋊D1465 |
| unambiguous semidirect product | C293⋊D65 |
| Fitting, socle, derived, Hall | C5×C13×C293 ⋊ C2 |
| Hall | C13×C293 ⋊ D5 |
| Hall | C5×C293 ⋊ D13 |
| Sylow | C293 ⋊ D65 |
| Hall | C5×C13 ⋊ D293 |
| Sylow | C13 ⋊ D1465 |
| Sylow | C5 ⋊ D3809 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C293 | C2 |
| LCS | G ▷ C5×C13×C293 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 311 |
| transitive degree | μt(G) = 19045 |
A minimal faithful permutation representation — 2 generators on 311 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);(2,5)(3,4)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(20,311)(21,310)(22,309)(23,308)(24,307)(25,306)(26,305)(27,304)(28,303)(29,302)(30,301)(31,300)(32,299)(33,298)(34,297)(35,296)(36,295)(37,294)(38,293)(39,292)(40,291)(41,290)(42,289)(43,288)(44,287)(45,286)(46,285)(47,284)(48,283)(49,282)(50,281)(51,280)(52,279)(53,278)(54,277)(55,276)(56,275)(57,274)(58,273)(59,272)(60,271)(61,270)(62,269)(63,268)(64,267)(65,266)(66,265)(67,264)(68,263)(69,262)(70,261)(71,260)(72,259)(73,258)(74,257)(75,256)(76,255)(77,254)(78,253)(79,252)(80,251)(81,250)(82,249)(83,248)(84,247)(85,246)(86,245)(87,244)(88,243)(89,242)(90,241)(91,240)(92,239)(93,238)(94,237)(95,236)(96,235)(97,234)(98,233)(99,232)(100,231)(101,230)(102,229)(103,228)(104,227)(105,226)(106,225)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)(113,218)(114,217)(115,216)(116,215)(117,214)(118,213)(119,212)(120,211)(121,210)(122,209)(123,208)(124,207)(125,206)(126,205)(127,204)(128,203)(129,202)(130,201)(131,200)(132,199)(133,198)(134,197)(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)(141,190)(142,189)(143,188)(144,187)(145,186)(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)(153,178)(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)Polycyclic presentation:
2,5,13,293|b^a=b^4,c^a=c^12,d^a=d^2929524 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38090, 8);