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D₃×C₁₉×C₁₂₁ #28352248

order	13794
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₁₂₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉×C₁₂₁
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₁₂₁)

Splittings

Fitting, Hall	C₃×C₁₉×C₁₂₁ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉×C₁₂₁
Hall	C₃×C₁₂₁ ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₁₂₁	D₃
commutator, hypocenter	C₃	C₂×C₁₉×C₁₂₁
Frattini	C₁₁	D₃×C₁₁×C₁₉
Fitting	C₃×C₁₉×C₁₂₁	C₂
socle	C₃×C₁₁×C₁₉	C₂×C₁₁
prime radical	D₃×C₁₁×C₁₉	C₁₁
cosocle	C₃×C₁₁	C₂×C₁₁×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₁₂₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6897

Conjugacy classes & character table

6897 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₁₉×C₁₂₁, D₃×C₁₉×D₁₂₁, D₃×D₂₂₉₉, …
maximal normal subgroup of	D₃×D₁₉×C₁₂₁, D₃×C₁₉×D₁₂₁, D₃×D₂₂₉₉, …
maximal quotient of	Dic₃×C₁₉×C₁₂₁, C₂×D₃×C₁₉×C₁₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13794, 9);