Finite Group Databasebeta

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C₉×C₁₉×D₄₁ #28380366

order	14022
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×D₄₁
unambiguous semidirect product	C₄₁⋊(C₂×C₉×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₉×C₄₁ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₄₁ ⋊ C₂×C₉
Hall	C₉×C₄₁ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₄₁
commutator, hypocenter	C₄₁	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₄₁
Fitting	C₉×C₁₉×C₄₁	C₂
socle	C₃×C₁₉×C₄₁	C₂×C₃
prime radical	C₃×C₁₉×D₄₁	C₃
cosocle	C₃×C₄₁	C₂×C₃×C₁₉
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7011

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₉×#4223, C₉×C₁₉⋊#4223, C₉×D₁₉×D₄₁, …
maximal normal subgroup of	C₉×C₁₉×#4223, C₉×C₁₉⋊#4223, C₉×D₁₉×D₄₁, …
maximal quotient of	C₉×C₁₉×Dic₄₁, C₂×C₉×C₁₉×D₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14022, 3);