Finite Group Databasebeta

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C₉×D₅×C₁₆₃ #28412686

order	14670
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₆₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅×C₁₆₃
unambiguous semidirect product	C₅⋊(C₂×C₉×C₁₆₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₆₃	D₅
commutator, hypocenter	C₅	C₂×C₉×C₁₆₃
Frattini	C₃	C₃×D₅×C₁₆₃
Fitting	C₅×C₉×C₁₆₃	C₂
socle	C₃×C₅×C₁₆₃	C₂×C₃
prime radical	C₃×D₅×C₁₆₃	C₃
cosocle	C₃×C₅	C₂×C₃×C₁₆₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₁₆₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7335

Conjugacy classes & character table

5868 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×AGL(1,𝔽₅)×C₁₆₃, C₉×C₁₆₃⋊AGL(1,𝔽₅), C₉×D₅×D₁₆₃, …
maximal normal subgroup of	C₉×AGL(1,𝔽₅)×C₁₆₃, C₉×C₁₆₃⋊AGL(1,𝔽₅), C₉×D₅×D₁₆₃, …
maximal quotient of	C₉×Dic₅×C₁₆₃, C₂×C₉×D₅×C₁₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14670, 4);