Finite Group Databasebeta

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C₃×A₄×C₁₉×C₄₉ #45691446

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉×C₄₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×A₄×C₁₉×C₄₉
unambiguous semidirect product	C₂²⋊(C₃²×C₁₉×C₄₉)
unambiguous semidirect product	(C₂²×C₃)⋊(C₃×C₁₉×C₄₉)

Splittings

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

Subgroups

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

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11172

Conjugacy classes & character table

11172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 244);