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C₉×D₄₄₉ #22549090

order	8082
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₄₄₉
unambiguous semidirect product	C₄₄₉⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₄₄₉ ⋊ C₂
derived, Sylow	C₄₄₉ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₄₄₉
commutator, hypocenter	C₄₄₉	C₂×C₉
Frattini	C₃	C₃×D₄₄₉
Fitting	C₉×C₄₄₉	C₂
socle	C₃×C₄₄₉	C₂×C₃
LCS	G ▷ C₄₄₉
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2034 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#14267798, C₉⋊#14267798, D₉×D₄₄₉, …
maximal normal subgroup of	C₉×#14267798, C₉⋊#14267798, D₉×D₄₄₉, …
maximal quotient of	C₉×Dic₄₄₉, C₂×C₉×D₄₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8082, 3);