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C₂×C₉×C₁₉×D₁₁ #21418985

order	7524
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×C₁₉×D₁₁
unambiguous semidirect product	C₁₁⋊(C₂²×C₉×C₁₉)
unambiguous semidirect product	(C₂×C₁₁)⋊(C₂×C₉×C₁₉)

Splittings

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

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₉×C₁₉×AGL(1,𝔽₁₁), C₉×D₅×C₁₉×D₁₁, C₂×C₉×C₁₉×D₅₅, …
maximal normal subgroup of	C₂×C₉×C₁₉×AGL(1,𝔽₁₁), C₂×C₅×C₉×C₁₉×D₁₁
maximal quotient of	C₉×D₅×C₁₉×D₁₁, C₂×C₉×C₁₉×D₅₅, C₂×C₅×C₉×C₁₉×D₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 29);