Finite Group Databasebeta

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A₄×C₁₉×C₁₂₁ #42119934

order	27588
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉×C₁₂₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₁₉×C₁₂₁
unambiguous semidirect product	C₂²⋊(C₃×C₁₉×C₁₂₁)
unambiguous semidirect product	(C₂²×C₁₂₁)⋊(C₃×C₁₉)

Splittings

Fitting, Hall	C₂²×C₁₉×C₁₂₁ ⋊ C₃
derived, Sylow	C₂² ⋊ C₃×C₁₉×C₁₂₁
Hall	C₂²×C₁₂₁ ⋊ C₃×C₁₉
Hall	C₂²×C₁₉ ⋊ C₃×C₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₁₂₁	A₄
commutator, hypocenter	C₂²	C₃×C₁₉×C₁₂₁
Frattini	C₁₁	C₁₁×A₄×C₁₉
Fitting	C₂²×C₁₉×C₁₂₁	C₃
socle	C₂²×C₁₁×C₁₉	C₃×C₁₁
prime radical	C₁₁×A₄×C₁₉	C₁₁
cosocle	C₂²×C₁₁	C₃×C₁₁×C₁₉
LCS	G ▷ C₂²
UCS	C₁ ◁ C₁₉×C₁₂₁

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9196

Conjugacy classes & character table

9196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 26);