Finite Group Databasebeta

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C₉×C₂₉×D₂₃ #26046383

order	12006
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₂₉×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂×C₉×C₂₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₉	D₂₃
commutator, hypocenter	C₂₃	C₂×C₉×C₂₉
Frattini	C₃	C₃×C₂₉×D₂₃
Fitting	C₉×C₂₃×C₂₉	C₂
socle	C₃×C₂₃×C₂₉	C₂×C₃
prime radical	C₃×C₂₉×D₂₃	C₃
cosocle	C₃×C₂₃	C₂×C₃×C₂₉
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₉×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3393 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×D₂₉, D₉×C₂₉×D₂₃, D₂₃×D₂₆₁, …
maximal normal subgroup of	C₉×D₂₃×D₂₉, D₉×C₂₉×D₂₃, D₂₃×D₂₆₁, …
maximal quotient of	C₉×C₂₉×Dic₂₃, C₂×C₉×C₂₉×D₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12006, 3);