D₁₅₀₂₁ #44473449

order	30042
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₀₂₁
unambiguous semidirect product	C₉⋊D₁₆₆₉
unambiguous semidirect product	C₁₆₆₉⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₆₆₉ ⋊ C₂
Sylow	C₁₆₆₉ ⋊ D₉
Sylow	C₉ ⋊ D₁₆₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₆₆₉	C₂
Frattini	C₃	D₅₀₀₇
socle	C₃×C₁₆₆₉	D₃
LCS	G ▷ C₉×C₁₆₆₉
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1678
transitive degree	μ_t(G) = 15021

A minimal faithful permutation representation — 2 generators on 1678 points:

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Polycyclic presentation:

2,3,1669,3|b^3=d^2,b^a=b^2d,c^a=c^1668,d^a=d^2

Conjugacy classes & character table

7512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₀₂₁
maximal normal subgroup of	C₂×D₁₅₀₂₁
maximal quotient of	Dic₁₅₀₂₁, C₂×D₁₅₀₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30042, 6);

D15021 #44473449