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C₁₉×C₂²⋊(C₃₁⋊C₃) #20296648

order	7068
isoclinism	isoclinic class of C₂²⋊(C₃₁⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

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

Splittings

Fitting, socle, Hall	C₂²×C₁₉×C₃₁ ⋊ C₃
derived, Hall	C₂²×C₃₁ ⋊ C₃×C₁₉
Hall	C₁₉×C₃₁ ⋊ A₄
Hall	C₂²×C₁₉ ⋊ C₃₁⋊C₃
Sylow	C₃₁ ⋊ A₄×C₁₉
Sylow	C₂² ⋊ C₁₉×C₃₁⋊C₃

Subgroups

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

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7068, 52);