C₉×D₂₅₃ #17986906

order	4554
isoclinism	isoclinic class of D₂₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₂₅₃
unambiguous semidirect product	C₁₁⋊(C₉×D₂₃)
unambiguous semidirect product	C₂₃⋊(C₉×D₁₁)

Splittings

Fitting, Hall	C₉×C₁₁×C₂₃ ⋊ C₂
derived, Hall	C₁₁×C₂₃ ⋊ C₂×C₉
Hall	C₉×C₂₃ ⋊ D₁₁
Hall	C₉×C₁₁ ⋊ D₂₃
Sylow	C₂₃ ⋊ C₉×D₁₁
Sylow	C₁₁ ⋊ C₉×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₂₅₃
commutator, hypocenter	C₁₁×C₂₃	C₂×C₉
Frattini	C₃	C₃×D₂₅₃
Fitting	C₉×C₁₁×C₂₃	C₂
socle, cosocle	C₃×C₁₁×C₂₃	C₂×C₃
prime radical	C₃×D₂₅₃	C₃
LCS	G ▷ C₁₁×C₂₃
UCS	C₁ ◁ C₉

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);(11,20)(12,19)(13,18)(14,17)(15,16)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

Conjugacy classes & character table

1152 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₂₅₃, C₉×D₁₂₆₅, C₉×C₂₃⋊AGL(1,𝔽₁₁), …
maximal normal subgroup of	C₅×C₉×D₂₅₃, C₉×C₂₃⋊AGL(1,𝔽₁₁), C₇×C₉×D₂₅₃
maximal quotient of	C₅×C₉×D₂₅₃, C₉×D₁₂₆₅, C₇×C₉×D₂₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 8);

C9×D253 #17986906