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C₉×C₁₉×D₁₁ #16836767

order	3762
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×D₁₁
unambiguous semidirect product	C₁₁⋊(C₂×C₉×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₁×C₁₉ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₉×C₁₉
Hall	C₁₁×C₁₉ ⋊ C₂×C₉
Hall	C₉×C₁₁ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₁₁
commutator, hypocenter	C₁₁	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₁₁
Fitting	C₉×C₁₁×C₁₉	C₂
socle	C₃×C₁₁×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×D₁₁	C₃
cosocle	C₃×C₁₁	C₂×C₃×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1881

A minimal faithful permutation representation — 2 generators on 39 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);(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×C₁₉×D₁₁, C₉×C₁₉×D₅₅, C₉×C₁₉×AGL(1,𝔽₁₁), …
maximal normal subgroup of	C₅×C₉×C₁₉×D₁₁, C₉×C₁₉×AGL(1,𝔽₁₁), C₇×C₉×C₁₉×D₁₁
maximal quotient of	C₅×C₉×C₁₉×D₁₁, C₉×C₁₉×D₅₅, C₇×C₉×C₁₉×D₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3762, 7);