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C₁₉×(C₃⋊D₃)⋊D₁₁ #21419057

order	7524
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×(C₃⋊D₃)⋊D₁₁
unambiguous semidirect product	(C₃⋊D₃)⋊(C₁₉×D₁₁)
unambiguous semidirect product	D₃₃⋊(D₃×C₁₉)

Splittings

Fitting, socle, Hall	C₃²×C₁₁×C₁₉ ⋊ C₂²
derived, Hall	C₃²×C₁₁ ⋊ C₂²×C₁₉
Hall	C₁₁×C₁₉ ⋊ D₃²
Hall	C₃²×C₁₉ ⋊ C₂×D₁₁
Sylow	C₁₁ ⋊ D₃²×C₁₉
Sylow	C₃² ⋊ C₂×C₁₉×D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	(C₃⋊D₃)⋊D₁₁
commutator, hypocenter	C₃²×C₁₁	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₉

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

741 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×(C₃⋊D₃)⋊AGL(1,𝔽₁₁), C₅×C₁₉×(C₃⋊D₃)⋊D₁₁, C₁₉×D₃₃⋊D₁₅, …
maximal normal subgroup of	C₁₉×(C₃⋊D₃)⋊AGL(1,𝔽₁₁), C₅×C₁₉×(C₃⋊D₃)⋊D₁₁
maximal quotient of	C₅×C₁₉×(C₃⋊D₃)⋊D₁₁, C₁₉×D₃₃⋊D₁₅, C₁₉×(C₃⋊D₃)⋊D₅₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 101);