Finite Group Databasebeta

← Prev (#34037827) Next (#34037829) →

C₉×C₁₉×AGL(1,𝔽₁₁) #34037828

order	18810
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₅×C₉×C₁₉)
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₂×C₉×C₁₉)
unambiguous semidirect product	(C₉×D₁₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₉×C₁₉×D₁₁)⋊C₅

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁	C₂×C₅×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×AGL(1,𝔽₁₁)
Fitting	C₉×C₁₁×C₁₉	C₂×C₅
socle	C₃×C₁₁×C₁₉	C₂×C₃×C₅
prime radical	C₃×C₁₉×AGL(1,𝔽₁₁)	C₃
cosocle	C₃×C₁₁	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₉×C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1881

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×AGL(1,𝔽₁₁), D₉×C₁₉×AGL(1,𝔽₁₁), AGL(1,𝔽₁₁)×D₁₇₁, …
maximal normal subgroup of	C₉×D₁₉×AGL(1,𝔽₁₁), D₉×C₁₉×AGL(1,𝔽₁₁), AGL(1,𝔽₁₁)×D₁₇₁, …
maximal quotient of	C₉×C₁₉×Dic₁₁⋊C₅, C₂×C₉×C₁₉×AGL(1,𝔽₁₁)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 21);