Finite Group Databasebeta

← Prev (#29503596) Next (#29503598) →

C₉×C₅⋊(C₁₃⋊D₁₃) #29503597

order	15210
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₉×C₅⋊(C₁₃⋊D₁₃)
unambiguous semidirect product	C₅⋊(C₉×C₁₃⋊D₁₃)

Splittings

Fitting, Hall	C₅×C₉×C₁₃² ⋊ C₂
derived, Hall	C₅×C₁₃² ⋊ C₂×C₉
Hall	C₉×C₁₃² ⋊ D₅
Sylow	C₁₃² ⋊ C₉×D₅
Hall	C₅×C₉ ⋊ C₁₃⋊D₁₃
Sylow	C₅ ⋊ C₉×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₅⋊(C₁₃⋊D₁₃)
commutator, hypocenter	C₅×C₁₃²	C₂×C₉
Frattini	C₃	C₃×C₅⋊(C₁₃⋊D₁₃)
Fitting	C₅×C₉×C₁₃²	C₂
socle, cosocle	C₃×C₅×C₁₃²	C₂×C₃
prime radical	C₃×C₅⋊(C₁₃⋊D₁₃)	C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₉

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7605

Conjugacy classes & character table

3816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#16810002, C₉×#16810003, C₉×#16810004, …
maximal normal subgroup of	C₉×#16810002, C₉×#16810003, C₉×#16810004, …
maximal quotient of	C₉×#16809991, C₂×C₉×C₅⋊(C₁₃⋊D₁₃)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 60);