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C₃×C₁₉×(C₄₉⋊C₃)⋊C₄ #45691285

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉×(C₄₉⋊C₃)⋊C₄
unambiguous semidirect product	(C₄₉⋊C₃)⋊(C₃×C₄×C₁₉)
unambiguous semidirect product	Dic₄₉⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×Dic₄₉)⋊(C₃×C₁₉)

Splittings

derived, Sylow	C₄₉ ⋊ C₃²×C₄×C₁₉
Hall	C₃×C₁₉×C₄₉⋊C₃ ⋊ C₄
Hall	C₁₉×Dic₄₉ ⋊ C₃²
Hall	C₁₉×C₄₉ ⋊ C₃²×C₄
Hall	C₃×C₄₉⋊C₃ ⋊ C₄×C₁₉
Hall	Dic₄₉ ⋊ C₃²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₄₉⋊C₃
commutator, hypocenter	C₄₉	C₃²×C₄×C₁₉
Frattini	C₂×C₇	C₃×C₁₉×AGL(1,𝔽₇)
Fitting	C₂×C₃×C₁₉×C₄₉	C₂×C₃
socle	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)
prime radical	C₂×C₃×C₁₉×C₄₉⋊C₃	C₂
cosocle	C₂×C₄₉	C₂×C₃²×C₁₉
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₃×C₁₉

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11172

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 83);