D₁₁₄₉₅ #37527359

order	22990
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₄₉₅
unambiguous semidirect product	C₅⋊D₂₂₉₉
unambiguous semidirect product	C₁₉⋊D₆₀₅
unambiguous semidirect product	C₁₂₁⋊D₉₅

Splittings

Fitting, derived, Hall	C₅×C₁₉×C₁₂₁ ⋊ C₂
Hall	C₁₉×C₁₂₁ ⋊ D₅
Hall	C₅×C₁₂₁ ⋊ D₁₉
Sylow	C₁₂₁ ⋊ D₉₅
Hall	C₅×C₁₉ ⋊ D₁₂₁
Sylow	C₁₉ ⋊ D₆₀₅
Sylow	C₅ ⋊ D₂₂₉₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₁₉×C₁₂₁	C₂
Frattini	C₁₁	D₁₀₄₅
socle	C₅×C₁₁×C₁₉	D₁₁
LCS	G ▷ C₅×C₁₉×C₁₂₁
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 145
transitive degree	μ_t(G) = 11495

A minimal faithful permutation representation — 2 generators on 145 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);(2,5)(3,4)(7,126)(8,125)(9,124)(10,123)(11,122)(12,121)(13,120)(14,119)(15,118)(16,117)(17,116)(18,115)(19,114)(20,113)(21,112)(22,111)(23,110)(24,109)(25,108)(26,107)(27,106)(28,105)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,98)(36,97)(37,96)(38,95)(39,94)(40,93)(41,92)(42,91)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)(128,145)(129,144)(130,143)(131,142)(132,141)(133,140)(134,139)(135,138)(136,137)

Polycyclic presentation:

2,5,11,19,11|c^11=e^10,b^a=b^4,c^a=c^10e,d^a=d^18,e^a=e^10

Conjugacy classes & character table

5749 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22990, 9);

D11495 #37527359