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A₄×C₄₉×C₁₉⋊C₃ #45691377

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	A₄×C₄₉×C₁₉⋊C₃
unambiguous semidirect product	(C₂²×C₁₉⋊C₃)⋊(C₃×C₄₉)
unambiguous semidirect product	(A₄×C₁₉)⋊(C₃×C₄₉)
unambiguous semidirect product	(C₂²⋊(C₁₉⋊C₃))⋊(C₃×C₄₉)

Splittings

Fitting, Hall	C₂²×C₁₉×C₄₉ ⋊ C₃²
derived, Hall	C₂²×C₁₉ ⋊ C₃²×C₄₉
Hall	C₁₉×C₄₉ ⋊ C₃×A₄
Hall	C₂²×C₄₉ ⋊ C₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₃×A₄×C₄₉
Sylow	C₂² ⋊ C₃×C₄₉×C₁₉⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉	A₄×C₁₉⋊C₃
commutator, hypocenter	C₂²×C₁₉	C₃²×C₄₉
Frattini	C₇	C₇×A₄×C₁₉⋊C₃
Fitting	C₂²×C₁₉×C₄₉	C₃²
socle, cosocle	C₂²×C₇×C₁₉	C₃²×C₇
prime radical	C₇×A₄×C₁₉⋊C₃	C₇
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₄₉

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3724

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 175);