D₉₇₂₉ #34085605

order	19458
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₇₂₉
unambiguous semidirect product	C₉⋊D₁₀₈₁
unambiguous semidirect product	C₂₃⋊D₄₂₃
unambiguous semidirect product	C₄₇⋊D₂₀₇

Splittings

Fitting, derived, Hall	C₉×C₂₃×C₄₇ ⋊ C₂
Hall	C₂₃×C₄₇ ⋊ D₉
Hall	C₉×C₄₇ ⋊ D₂₃
Hall	C₉×C₂₃ ⋊ D₄₇
Sylow	C₄₇ ⋊ D₂₀₇
Sylow	C₂₃ ⋊ D₄₂₃
Sylow	C₉ ⋊ D₁₀₈₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₃×C₄₇	C₂
Frattini	C₃	D₃₂₄₃
socle	C₃×C₂₃×C₄₇	D₃
LCS	G ▷ C₉×C₂₃×C₄₇
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 9729

A minimal faithful permutation representation — 2 generators on 79 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);(2,9)(3,8)(4,7)(5,6)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(34,79)(35,78)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Polycyclic presentation:

2,3,23,47,3|b^3=e^2,b^a=b^2e,c^a=c^22,d^a=d^46,e^a=e^2

Conjugacy classes & character table

4866 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉₁₈₇
maximal quotient of	D₂₉₁₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19458, 9);

D9729 #34085605