D₁₆₆₄₁ #45685437

order	33282
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₆₄₁
unambiguous semidirect product	C₉⋊D₁₈₄₉
unambiguous semidirect product	C₁₈₄₉⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₈₄₉ ⋊ C₂
Sylow	C₁₈₄₉ ⋊ D₉
Sylow	C₉ ⋊ D₁₈₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₈₄₉	C₂
Frattini, socle	C₃×C₄₃	D₁₂₉
LCS	G ▷ C₉×C₁₈₄₉
UCS	C₁

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1858
transitive degree	μ_t(G) = 16641

A minimal faithful permutation representation — 2 generators on 1858 points:

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Polycyclic presentation:

2,3,43,3,43|b^3=d^2,c^43=e^42,b^a=b^2d,c^a=c^42e,d^a=d^2,e^a=e^42

Conjugacy classes & character table

8322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33282, 6);

D16641 #45685437