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C₁₉×C₄₃⋊C₉ #20301348

order	7353
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

969 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×C₄₃⋊C₉, C₁₉×D₄₃⋊C₉, D₁₉×C₄₃⋊C₉, …
maximal normal subgroup of	C₂×C₁₉×C₄₃⋊C₉, C₁₉×D₄₃⋊C₉, D₁₉×C₄₃⋊C₉, …
maximal quotient of	C₂×C₁₉×C₄₃⋊C₉, C₁₉×C₂²⋊(C₄₃⋊C₉), C₅×C₁₉×C₄₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7353, 3);