Finite Group Databasebeta

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C₃×C₁₉×C₄₃⋊C₃ #20301359

order	7353
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉×C₄₃⋊C₃
unambiguous semidirect product	C₄₃⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×C₄₃)⋊(C₃×C₁₉)

Splittings

Fitting, socle	C₃×C₁₉×C₄₃ ⋊ C₃
derived, Sylow	C₄₃ ⋊ C₃²×C₁₉
Hall	C₁₉×C₄₃ ⋊ C₃²

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

969 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₁₉×D₄₃⋊C₃, C₃×(C₄₃⋊C₃)⋊D₁₉, C₃×D₁₉×C₄₃⋊C₃, …
maximal normal subgroup of	C₃×C₁₉×D₄₃⋊C₃, C₃×(C₄₃⋊C₃)⋊D₁₉, C₃×D₁₉×C₄₃⋊C₃, …
maximal quotient of	C₂×C₃×C₁₉×C₄₃⋊C₃, A₄×C₁₉×C₄₃⋊C₃, C₃×C₁₉×C₂²⋊(C₄₃⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7353, 14);