Finite Group Databasebeta

← Prev (#28408165) Next (#28408167) →

C₉×D₁₃×D₃₁ #28408166

order	14508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₃×D₃₁

Splittings

Fitting, Hall	C₉×C₁₃×C₃₁ ⋊ C₂²
derived, Hall	C₁₃×C₃₁ ⋊ C₂²×C₉
Hall	C₉×C₃₁ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₃₁
Sylow	C₃₁ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₃₁
commutator, hypocenter	C₁₃×C₃₁	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₃₁
Fitting	C₉×C₁₃×C₃₁	C₂²
socle, cosocle	C₃×C₁₃×C₃₁	C₂²×C₃
prime radical	C₃×D₁₃×D₃₁	C₃
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3627

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14508, 52);