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D₉×C₁₉×D₁₁ #21418977

order	7524
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₉×C₁₉×D₁₁
unambiguous semidirect product	(C₁₁×D₉)⋊(C₂×C₁₉)
unambiguous semidirect product	(C₉×D₁₁)⋊(C₂×C₁₉)
unambiguous semidirect product	D₉₉⋊(C₂×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₁×C₁₉ ⋊ C₂²
derived, Hall	C₉×C₁₁ ⋊ C₂²×C₁₉
Hall	C₁₁×C₁₉ ⋊ C₂×D₉
Hall	C₉×C₁₉ ⋊ C₂×D₁₁
Sylow	C₁₁ ⋊ C₂×D₉×C₁₉
Sylow	C₉ ⋊ C₂×C₁₉×D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₉×D₁₁
commutator, hypocenter	C₉×C₁₁	C₂²×C₁₉
Frattini	C₃	D₃×C₁₉×D₁₁
Fitting	C₉×C₁₁×C₁₉	C₂²
socle	C₃×C₁₁×C₁₉	C₂×D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

798 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×C₁₉×AGL(1,𝔽₁₁), C₅×D₉×C₁₉×D₁₁, C₁₉×D₁₁×D₄₅, …
maximal normal subgroup of	D₉×C₁₉×AGL(1,𝔽₁₁), C₅×D₉×C₁₉×D₁₁
maximal quotient of	C₅×D₉×C₁₉×D₁₁, C₁₉×D₁₁×D₄₅, D₉×C₁₉×D₅₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 21);