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D₃×C₁₉×C₄₃ #19096719

order	4902
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉×C₄₃
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₄₃)

Splittings

Fitting, socle, Hall	C₃×C₁₉×C₄₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉×C₄₃
Hall	C₃×C₄₃ ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₄₃	D₃
commutator, hypocenter	C₃	C₂×C₁₉×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₄₃

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2451 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₁₉×C₄₃, D₃×C₁₉×C₄₃⋊C₃, D₃×C₄₃×C₁₉⋊C₃, …
maximal normal subgroup of	D₃×C₁₉×C₄₃⋊C₃, D₃×C₄₃×C₁₉⋊C₃, D₃×#14578576, …
maximal quotient of	D₉×C₁₉×C₄₃, C₃⋊D₃×C₁₉×C₄₃, C₃×D₃×C₁₉×C₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4902, 9);