Finite Group Databasebeta

← Prev (#28408013) Next (#28408015) →

C₅×C₉×D₁₆₁ #28408014

order	14490
isoclinism	isoclinic class of D₁₆₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₉×D₁₆₁
unambiguous semidirect product	C₂₃⋊(C₅×C₉×D₇)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₁₆₁
commutator, hypocenter	C₇×C₂₃	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₁₆₁
Fitting	C₅×C₇×C₉×C₂₃	C₂
socle	C₃×C₅×C₇×C₂₃	C₂×C₃
prime radical	C₃×C₅×D₁₆₁	C₃
cosocle	C₃×C₇×C₂₃	C₂×C₃×C₅
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₅×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7245

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₇×D₂₃, C₉×D₅×D₁₆₁, C₉×D₃₅⋊D₂₃, …
maximal normal subgroup of	C₅×C₉×D₇×D₂₃, C₉×D₅×D₁₆₁, C₉×D₃₅⋊D₂₃, …
maximal quotient of	C₅×C₉×Dic₁₆₁, C₂×C₅×C₉×D₁₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 5);