D₁₆₀₈₃ #44565509

order	32166
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₀₈₃
unambiguous semidirect product	C₉⋊D₁₇₈₇
unambiguous semidirect product	C₁₇₈₇⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₇₈₇ ⋊ C₂
Sylow	C₁₇₈₇ ⋊ D₉
Sylow	C₉ ⋊ D₁₇₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₇₈₇	C₂
Frattini	C₃	D₅₃₆₁
socle	C₃×C₁₇₈₇	D₃
LCS	G ▷ C₉×C₁₇₈₇
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1796
transitive degree	μ_t(G) = 16083

A minimal faithful permutation representation — 2 generators on 1796 points:

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Polycyclic presentation:

2,3,1787,3|b^3=d^2,b^a=b^2d,c^a=c^1786,d^a=d^2

Conjugacy classes & character table

8043 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₀₈₃
maximal normal subgroup of	C₂×D₁₆₀₈₃
maximal quotient of	Dic₁₆₀₈₃, C₂×D₁₆₀₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32166, 4);

D16083 #44565509