D₁₁₄₃₉ #37504254

order	22878
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₄₃₉
unambiguous semidirect product	C₉⋊D₁₂₇₁
unambiguous semidirect product	C₃₁⋊D₃₆₉
unambiguous semidirect product	C₄₁⋊D₂₇₉

Splittings

Fitting, derived, Hall	C₉×C₃₁×C₄₁ ⋊ C₂
Hall	C₃₁×C₄₁ ⋊ D₉
Hall	C₉×C₄₁ ⋊ D₃₁
Hall	C₉×C₃₁ ⋊ D₄₁
Sylow	C₄₁ ⋊ D₂₇₉
Sylow	C₃₁ ⋊ D₃₆₉
Sylow	C₉ ⋊ D₁₂₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₃₁×C₄₁	C₂
Frattini	C₃	D₃₈₁₃
socle	C₃×C₃₁×C₄₁	D₃
LCS	G ▷ C₉×C₃₁×C₄₁
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 11439

A minimal faithful permutation representation — 2 generators on 81 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);(2,9)(3,8)(4,7)(5,6)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Polycyclic presentation:

2,3,31,41,3|b^3=e^2,b^a=b^2e,c^a=c^30,d^a=d^40,e^a=e^2

Conjugacy classes & character table

5721 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22878, 9);

D11439 #37504254