C₁₁×D₉×C₂₃ #17986907

order	4554
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₉×C₂₃
unambiguous semidirect product	C₉⋊(C₂×C₁₁×C₂₃)

Splittings

Fitting, Hall	C₉×C₁₁×C₂₃ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₁×C₂₃
Hall	C₉×C₂₃ ⋊ C₂×C₁₁
Hall	C₉×C₁₁ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₁×C₂₃
Frattini	C₃	D₃×C₁₁×C₂₃
Fitting	C₉×C₁₁×C₂₃	C₂
socle	C₃×C₁₁×C₂₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₁×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2277

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(13,20)(14,19)(15,18)(16,17)

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₁₁×D₉×C₂₃, C₁₁×C₂₃×D₄₅, D₉×C₂₃×C₁₁⋊C₅, …
maximal normal subgroup of	C₅×C₁₁×D₉×C₂₃, D₉×C₂₃×C₁₁⋊C₅, C₇×C₁₁×D₉×C₂₃
maximal quotient of	C₅×C₁₁×D₉×C₂₃, C₁₁×C₂₃×D₄₅, C₇×C₁₁×D₉×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 9);

C11×D9×C23 #17986907