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C₉×D₆₆₇ #26046384

order	12006
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₆₆₇
unambiguous semidirect product	C₂₃⋊(C₉×D₂₉)
unambiguous semidirect product	C₂₉⋊(C₉×D₂₃)

Splittings

Fitting, Hall	C₉×C₂₃×C₂₉ ⋊ C₂
derived, Hall	C₂₃×C₂₉ ⋊ C₂×C₉
Hall	C₉×C₂₉ ⋊ D₂₃
Hall	C₉×C₂₃ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₉×D₂₃
Sylow	C₂₃ ⋊ C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₆₆₇
commutator, hypocenter	C₂₃×C₂₉	C₂×C₉
Frattini	C₃	C₃×D₆₆₇
Fitting	C₉×C₂₃×C₂₉	C₂
socle, cosocle	C₃×C₂₃×C₂₉	C₂×C₃
prime radical	C₃×D₆₆₇	C₃
LCS	G ▷ C₂₃×C₂₉
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3015 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×D₂₉, D₉×D₆₆₇, D₂₀₇⋊D₂₉, …
maximal normal subgroup of	C₉×D₂₃×D₂₉, D₉×D₆₆₇, D₂₀₇⋊D₂₉, …
maximal quotient of	C₉×Dic₆₆₇, C₂×C₉×D₆₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12006, 4);