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C₉×C₂₃×D₂₃ #23749012

order	9522
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

Fitting, Hall	C₉×C₂₃² ⋊ C₂
derived	C₂₃ ⋊ C₂×C₉×C₂₃
Sylow	C₂₃² ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₃	D₂₃
commutator, hypocenter	C₂₃	C₂×C₉×C₂₃
Frattini	C₃	C₃×C₂₃×D₂₃
Fitting	C₉×C₂₃²	C₂
socle	C₃×C₂₃²	C₂×C₃
prime radical	C₃×C₂₃×D₂₃	C₃
cosocle	C₃×C₂₃	C₂×C₃×C₂₃
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₉×C₂₃

57 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃², D₉×C₂₃×D₂₃, D₂₃×D₂₀₇, …
maximal normal subgroup of	C₉×D₂₃², D₉×C₂₃×D₂₃, D₂₃×D₂₀₇, …
maximal quotient of	C₉×C₂₃×Dic₂₃, C₂×C₉×C₂₃×D₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9522, 15);