Finite Group Databasebeta

← Prev (#28330871) Next (#28330873) →

C₉×D₁₃×D₂₉ #28330872

order	13572
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₃×D₂₉

Splittings

Fitting, Hall	C₉×C₁₃×C₂₉ ⋊ C₂²
derived, Hall	C₁₃×C₂₉ ⋊ C₂²×C₉
Hall	C₉×C₂₉ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₂₉
commutator, hypocenter	C₁₃×C₂₉	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₂₉
Fitting	C₉×C₁₃×C₂₉	C₂²
socle, cosocle	C₃×C₁₃×C₂₉	C₂²×C₃
prime radical	C₃×D₁₃×D₂₉	C₃
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3393

Conjugacy classes & character table

1152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 30);