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C₁₉×D₄₃⋊C₉ #28413657

order	14706
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₄₃⋊C₉
unambiguous semidirect product	D₄₃⋊(C₉×C₁₉)
unambiguous semidirect product	(C₄₃⋊C₉)⋊(C₂×C₁₉)

Splittings

derived, Sylow	C₄₃ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₄₃⋊C₉ ⋊ C₂
Hall	C₁₉×D₄₃ ⋊ C₉
Hall	C₁₉×C₄₃ ⋊ C₂×C₉
Hall	C₄₃⋊C₉ ⋊ C₂×C₁₉
Hall	D₄₃ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₄₃⋊C₃
commutator, hypocenter	C₄₃	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×D₄₃⋊C₃
Fitting, socle	C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₃×C₁₉×D₄₃	C₃
cosocle	C₃×C₄₃	C₂×C₃×C₁₉
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7353

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₉×D₄₃⋊C₉, C₂×C₁₉×D₄₃⋊C₉
maximal normal subgroup of	D₁₉×D₄₃⋊C₉, C₂×C₁₉×D₄₃⋊C₉
maximal quotient of	C₁₉×Dic₄₃⋊C₉, C₂×C₁₉×D₄₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14706, 13);