Finite Group Databasebeta

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C₅×C₉×D₁₆₃ #28412685

order	14670
isoclinism	isoclinic class of D₁₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₉×D₁₆₃

Splittings

Fitting, Hall	C₅×C₉×C₁₆₃ ⋊ C₂
derived, Sylow	C₁₆₃ ⋊ C₂×C₅×C₉
Hall	C₉×C₁₆₃ ⋊ C₂×C₅
Hall	C₅×C₁₆₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₁₆₃
commutator, hypocenter	C₁₆₃	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₁₆₃
Fitting	C₅×C₉×C₁₆₃	C₂
socle	C₃×C₅×C₁₆₃	C₂×C₃
prime radical	C₃×C₅×D₁₆₃	C₃
cosocle	C₃×C₁₆₃	C₂×C₃×C₅
LCS	G ▷ C₁₆₃
UCS	C₁ ◁ C₅×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7335

Conjugacy classes & character table

3735 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₅×D₁₆₃, C₅×D₉×D₁₆₃, D₄₅×D₁₆₃, …
maximal normal subgroup of	C₉×D₅×D₁₆₃, C₅×D₉×D₁₆₃, D₄₅×D₁₆₃, …
maximal quotient of	C₅×C₉×Dic₁₆₃, C₂×C₅×C₉×D₁₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14670, 3);