Finite Group Databasebeta

← Prev (#21418963) Next (#21418965) →

C₉×Dic₂₀₉ #21418964

order	7524
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×Dic₂₀₉
unambiguous semidirect product	C₁₁⋊(C₉×Dic₁₉)

Splittings

derived, Hall	C₁₁×C₁₉ ⋊ C₄×C₉
Hall	C₉×C₁₁×C₁₉ ⋊ C₄
Hall	C₉×C₁₉ ⋊ Dic₁₁
Hall	C₉×C₁₁ ⋊ Dic₁₉
Sylow	C₁₉ ⋊ C₉×Dic₁₁
Sylow	C₁₁ ⋊ C₉×Dic₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₂₀₉
commutator, hypocenter	C₁₁×C₁₉	C₄×C₉
Frattini	C₂×C₃	C₃×D₂₀₉
Fitting	C₂×C₉×C₁₁×C₁₉	C₂
socle	C₂×C₃×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1908 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×Dic₂₀₉, C₉×Dic₁₀₄₅, C₉×C₁₉⋊(Dic₁₁⋊C₅), …
maximal normal subgroup of	C₅×C₉×Dic₂₀₉, C₉×C₁₉⋊(Dic₁₁⋊C₅)
maximal quotient of	C₅×C₉×Dic₂₀₉, C₉×Dic₁₀₄₅, C₉×C₁₁⋊(C₁₉⋊AGL(1,𝔽₅))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 8);