C₁₁×D₂₀₇ #17986908

order	4554
isoclinism	isoclinic class of D₂₀₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₂₀₇
unambiguous semidirect product	C₉⋊(C₁₁×D₂₃)

Splittings

Fitting, Hall	C₉×C₁₁×C₂₃ ⋊ C₂
derived, Hall	C₉×C₂₃ ⋊ C₂×C₁₁
Hall	C₁₁×C₂₃ ⋊ D₉
Hall	C₉×C₁₁ ⋊ D₂₃
Sylow	C₂₃ ⋊ C₁₁×D₉
Sylow	C₉ ⋊ C₁₁×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₂₀₇
commutator, cosocle, hypocenter	C₉×C₂₃	C₂×C₁₁
Frattini	C₃	C₁₁×D₆₉
Fitting	C₉×C₁₁×C₂₃	C₂
socle	C₃×C₁₁×C₂₃	D₃
LCS	G ▷ C₉×C₂₃
UCS	C₁ ◁ C₁₁

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)(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

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₁₁×D₂₀₇, C₁₁×D₁₀₃₅, C₁₁⋊C₅×D₂₀₇, …
maximal normal subgroup of	C₅×C₁₁×D₂₀₇, C₁₁⋊C₅×D₂₀₇, C₇×C₁₁×D₂₀₇
maximal quotient of	C₅×C₁₁×D₂₀₇, C₁₁×D₁₀₃₅, C₇×C₁₁×D₂₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 10);

C11×D207 #17986908