D₁₂₁₉₅ #37567252

order	24390
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₁₉₅
unambiguous semidirect product	C₅⋊D₂₄₃₉
unambiguous semidirect product	C₉⋊D₁₃₅₅
unambiguous semidirect product	C₂₇₁⋊D₄₅

Splittings

Fitting, derived, Hall	C₅×C₉×C₂₇₁ ⋊ C₂
Hall	C₉×C₂₇₁ ⋊ D₅
Hall	C₅×C₂₇₁ ⋊ D₉
Sylow	C₂₇₁ ⋊ D₄₅
Hall	C₅×C₉ ⋊ D₂₇₁
Sylow	C₉ ⋊ D₁₃₅₅
Sylow	C₅ ⋊ D₂₄₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₂₇₁	C₂
Frattini	C₃	D₄₀₆₅
socle	C₃×C₅×C₂₇₁	D₃
LCS	G ▷ C₅×C₉×C₂₇₁
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 285
transitive degree	μ_t(G) = 12195

A minimal faithful permutation representation — 2 generators on 285 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);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,285)(17,284)(18,283)(19,282)(20,281)(21,280)(22,279)(23,278)(24,277)(25,276)(26,275)(27,274)(28,273)(29,272)(30,271)(31,270)(32,269)(33,268)(34,267)(35,266)(36,265)(37,264)(38,263)(39,262)(40,261)(41,260)(42,259)(43,258)(44,257)(45,256)(46,255)(47,254)(48,253)(49,252)(50,251)(51,250)(52,249)(53,248)(54,247)(55,246)(56,245)(57,244)(58,243)(59,242)(60,241)(61,240)(62,239)(63,238)(64,237)(65,236)(66,235)(67,234)(68,233)(69,232)(70,231)(71,230)(72,229)(73,228)(74,227)(75,226)(76,225)(77,224)(78,223)(79,222)(80,221)(81,220)(82,219)(83,218)(84,217)(85,216)(86,215)(87,214)(88,213)(89,212)(90,211)(91,210)(92,209)(93,208)(94,207)(95,206)(96,205)(97,204)(98,203)(99,202)(100,201)(101,200)(102,199)(103,198)(104,197)(105,196)(106,195)(107,194)(108,193)(109,192)(110,191)(111,190)(112,189)(113,188)(114,187)(115,186)(116,185)(117,184)(118,183)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,170)(132,169)(133,168)(134,167)(135,166)(136,165)(137,164)(138,163)(139,162)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)

Polycyclic presentation:

2,3,5,271,3|b^3=e^2,b^a=b^2e,c^a=c^4,d^a=d^270,e^a=e^2

Conjugacy classes & character table

6099 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24390, 11);

D12195 #37567252