Finite Group Databasebeta

← Prev (#34090605) Next (#34090607) →

C₉×D₁₉×D₂₉ #34090606

order	19836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₉×D₂₉

Splittings

Fitting, Hall	C₉×C₁₉×C₂₉ ⋊ C₂²
derived, Hall	C₁₉×C₂₉ ⋊ C₂²×C₉
Hall	C₉×C₂₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₉×D₂₉
commutator, hypocenter	C₁₉×C₂₉	C₂²×C₉
Frattini	C₃	C₃×D₁₉×D₂₉
Fitting	C₉×C₁₉×C₂₉	C₂²
socle, cosocle	C₃×C₁₉×C₂₉	C₂²×C₃
prime radical	C₃×D₁₉×D₂₉	C₃
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4959

Conjugacy classes & character table

1584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 22);