D₁₂₁₄₁ #37566327

order	24282
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₁₄₁
unambiguous semidirect product	C₉⋊D₁₃₄₉
unambiguous semidirect product	C₁₉⋊D₆₃₉
unambiguous semidirect product	C₇₁⋊D₁₇₁

Splittings

Fitting, derived, Hall	C₉×C₁₉×C₇₁ ⋊ C₂
Hall	C₁₉×C₇₁ ⋊ D₉
Hall	C₉×C₇₁ ⋊ D₁₉
Hall	C₉×C₁₉ ⋊ D₇₁
Sylow	C₇₁ ⋊ D₁₇₁
Sylow	C₁₉ ⋊ D₆₃₉
Sylow	C₉ ⋊ D₁₃₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉×C₇₁	C₂
Frattini	C₃	D₄₀₄₇
socle	C₃×C₁₉×C₇₁	D₃
LCS	G ▷ C₉×C₁₉×C₇₁
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 99
transitive degree	μ_t(G) = 12141

A minimal faithful permutation representation — 2 generators on 99 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);(2,9)(3,8)(4,7)(5,6)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Polycyclic presentation:

2,3,19,71,3|b^3=e^2,b^a=b^2e,c^a=c^18,d^a=d^70,e^a=e^2

Conjugacy classes & character table

6072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24282, 9);

D12141 #37566327