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C₃×C₄₉×C₂²⋊(C₁₉⋊C₃) #45691445

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

Aliases

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

Splittings

Fitting	C₂²×C₃×C₁₉×C₄₉ ⋊ C₃
derived, Hall	C₂²×C₁₉ ⋊ C₃²×C₄₉
Hall	C₂²×C₁₉×C₄₉ ⋊ C₃²
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	C₃×C₄₉	C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₉	C₃²×C₄₉
Frattini	C₇	C₃×C₇×C₂²⋊(C₁₉⋊C₃)
Fitting	C₂²×C₃×C₁₉×C₄₉	C₃
socle	C₂²×C₃×C₇×C₁₉	C₃×C₇
prime radical	C₃×C₇×C₂²⋊(C₁₉⋊C₃)	C₇
cosocle	C₂²×C₇×C₁₉	C₃²×C₇
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₄₉

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11172

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 243);