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C₃×C₄×C₁₉×C₄₃⋊C₃ #44440951

order	29412
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₄×C₁₉×C₄₃⋊C₃
unambiguous semidirect product	(C₄×C₄₃)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×C₄×C₄₃)⋊(C₃×C₁₉)

Splittings

Fitting	C₃×C₄×C₁₉×C₄₃ ⋊ C₃
derived, Sylow	C₄₃ ⋊ C₃²×C₄×C₁₉
Hall	C₄×C₁₉×C₄₃ ⋊ C₃²
Hall	C₁₉×C₄₃ ⋊ C₃²×C₄
Hall	C₄×C₄₃ ⋊ C₃²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₉	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₃²×C₄×C₁₉
Frattini	C₂	C₂×C₃×C₁₉×C₄₃⋊C₃
Fitting	C₃×C₄×C₁₉×C₄₃	C₃
socle	C₂×C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₄₃⋊C₃	C₂
cosocle	C₂×C₄₃	C₂×C₃²×C₁₉
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₄×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9804

Conjugacy classes & character table

3876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29412, 113);