Finite Group Databasebeta

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D₃×C₁₉×C₇₉ #22583027

order	9006
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉×C₇₉
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₇₉)

Splittings

Fitting, socle, Hall	C₃×C₁₉×C₇₉ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉×C₇₉
Hall	C₃×C₇₉ ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₇₉	D₃
commutator, hypocenter	C₃	C₂×C₁₉×C₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₇₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₇₉

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4503 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₁₉×D₇₉, D₃×D₁₉×C₇₉, D₃×D₁₅₀₁, …
maximal normal subgroup of	D₃×C₁₉×D₇₉, D₃×D₁₉×C₇₉, D₃×D₁₅₀₁, …
maximal quotient of	Dic₃×C₁₉×C₇₉, C₂×D₃×C₁₉×C₇₉, D₉×C₁₉×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9006, 9);