Finite Group Databasebeta

← Prev (#28408016) Next (#28408018) →

C₉×C₂₃×D₃₅ #28408017

order	14490
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₂₃×D₃₅
unambiguous semidirect product	C₅⋊(C₉×D₇×C₂₃)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₃	D₃₅
commutator, hypocenter	C₅×C₇	C₂×C₉×C₂₃
Frattini	C₃	C₃×C₂₃×D₃₅
Fitting	C₅×C₇×C₉×C₂₃	C₂
socle	C₃×C₅×C₇×C₂₃	C₂×C₃
prime radical	C₃×C₂₃×D₃₅	C₃
cosocle	C₃×C₅×C₇	C₂×C₃×C₂₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₉×C₂₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7245

Conjugacy classes & character table

3933 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×D₃₅, C₉×D₅×D₇×C₂₃, C₉×D₃₅⋊D₂₃, …
maximal normal subgroup of	C₉×D₂₃×D₃₅, C₉×D₅×D₇×C₂₃, C₉×D₃₅⋊D₂₃, …
maximal quotient of	C₉×C₂₃×Dic₃₅, C₂×C₉×C₂₃×D₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 8);