C₃²×C₁₁×D₂₃ #17986918

order	4554
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₁ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₃²×C₁₁×D₂₃

Splittings

Fitting, socle, Hall	C₃²×C₁₁×C₂₃ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂×C₃²×C₁₁
Hall	C₁₁×C₂₃ ⋊ C₂×C₃²
Hall	C₃²×C₂₃ ⋊ C₂×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₁₁	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₃²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₃²×C₁₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 2277

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(4,5,6)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×D₂₃×C₁₁⋊C₅, C₃²×C₅×C₁₁×D₂₃, C₃²×C₁₁×D₁₁₅, …
maximal normal subgroup of	C₃²×D₂₃×C₁₁⋊C₅, C₃²×C₅×C₁₁×D₂₃, C₃²×C₇×C₁₁×D₂₃
maximal quotient of	C₃²×C₅×C₁₁×D₂₃, C₃²×C₁₁×D₁₁₅, C₃×C₁₁×ΓL(1,𝔽₈)⋊D₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 20);

C32×C11×D23 #17986918