Finite Group Databasebeta

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A₄×C₁₉×C₃₁ #20296649

order	7068
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₁₉×C₃₁
unambiguous semidirect product	C₂²⋊(C₃×C₁₉×C₃₁)

Splittings

Fitting, socle, Hall	C₂²×C₁₉×C₃₁ ⋊ C₃
derived, Sylow	C₂² ⋊ C₃×C₁₉×C₃₁
Hall	C₂²×C₃₁ ⋊ C₃×C₁₉
Hall	C₂²×C₁₉ ⋊ C₃×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₃₁	A₄
commutator, hypocenter	C₂²	C₃×C₁₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉×C₃₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₁₉×C₃₁

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2356 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	A₄×C₁₉×C₃₁⋊C₃, A₄×C₃₁×C₁₉⋊C₃, A₄×#13183714, …
maximal normal subgroup of	A₄×C₁₉×C₃₁⋊C₃, A₄×C₃₁×C₁₉⋊C₃, A₄×#13183714, …
maximal quotient of	C₁₉×C₃₁×C₂²⋊C₉, C₃×A₄×C₁₉×C₃₁, C₅×A₄×C₁₉×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7068, 53);