Finite Group Databasebeta

← Prev (#23749012) Next (#23749014) →

C₉×C₂₃⋊D₂₃ #23749013

order	9522
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₂₃

Aliases

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

Splittings

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

Subgroups

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

156 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃², C₉×#14523747, D₉×C₂₃⋊D₂₃, …
maximal normal subgroup of	C₉×D₂₃², C₉×#14523747, D₉×C₂₃⋊D₂₃, …
maximal quotient of	C₉×C₂₃⋊Dic₂₃, C₂×C₉×C₂₃⋊D₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9522, 16);