Finite Group Databasebeta

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C₂×C₁₉×C₄₃⋊C₃ #19096712

order	4902
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉⋊C₃×C₄₃⋊C₃, D₃×C₁₉×C₄₃⋊C₃, C₂×C₃×C₁₉×C₄₃⋊C₃, …
maximal normal subgroup of	C₂×C₁₉⋊C₃×C₄₃⋊C₃, C₂×C₃×C₁₉×C₄₃⋊C₃, C₂×C₅×C₁₉×C₄₃⋊C₃, …
maximal quotient of	C₂×C₁₉×C₄₃⋊C₉, D₃×C₁₉×C₄₃⋊C₃, C₂×C₃×C₁₉×C₄₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4902, 2);