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C₉×D₁₁×D₁₉ #21418974

order	7524
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₁×D₁₉

Splittings

Fitting, Hall	C₉×C₁₁×C₁₉ ⋊ C₂²
derived, Hall	C₁₁×C₁₉ ⋊ C₂²×C₉
Hall	C₉×C₁₉ ⋊ C₂×D₁₁
Hall	C₉×C₁₁ ⋊ C₂×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×D₁₁
Sylow	C₁₁ ⋊ C₂×C₉×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₁×D₁₉
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₉
Frattini	C₃	C₃×D₁₁×D₁₉
Fitting	C₉×C₁₁×C₁₉	C₂²
socle	C₃×C₁₁×C₁₉	C₂²×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

693 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×D₁₉×AGL(1,𝔽₁₁), C₅×C₉×D₁₁×D₁₉, C₉×D₁₉×D₅₅, …
maximal normal subgroup of	C₉×D₁₉×AGL(1,𝔽₁₁), C₅×C₉×D₁₁×D₁₉
maximal quotient of	C₅×C₉×D₁₁×D₁₉, C₉×D₁₉×D₅₅, C₉×D₁₁×D₉₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 18);