C₉×D₂₃ #88024

order	414
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 207

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,4,3,5,7,6,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);(10,11,13,15,17,19,21,23,25,27,29,31,32,30,28,26,24,22,20,18,16,14,12)

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₂₃, C₂×C₉×D₂₃, C₂₇×D₂₃, …
maximal normal subgroup of	D₉×D₂₃, C₂×C₉×D₂₃, C₂₇×D₂₃, …
maximal quotient of	C₉×Dic₂₃, C₂×C₉×D₂₃, C₂₇×D₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(414, 2);

C9×D23 #88024

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₉×D₂₃ #88024