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C₉×D₈₀₅ #28408018

order	14490
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₈₀₅
unambiguous semidirect product	C₅⋊(C₉×D₁₆₁)
unambiguous semidirect product	C₂₃⋊(C₉×D₃₅)

Splittings

Fitting, Hall	C₅×C₇×C₉×C₂₃ ⋊ C₂
derived, Hall	C₅×C₇×C₂₃ ⋊ C₂×C₉
Hall	C₇×C₉×C₂₃ ⋊ D₅
Hall	C₅×C₉×C₂₃ ⋊ D₇
Hall	C₅×C₇×C₉ ⋊ D₂₃
Hall	C₉×C₂₃ ⋊ D₃₅
Hall	C₇×C₂₃ ⋊ C₉×D₅
Hall	C₅×C₂₃ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₁₅
Hall	C₅×C₉ ⋊ D₁₆₁
Hall	C₅×C₇ ⋊ C₉×D₂₃
Sylow	C₂₃ ⋊ C₉×D₃₅
Sylow	C₇ ⋊ C₉×D₁₁₅
Sylow	C₅ ⋊ C₉×D₁₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₀₅
commutator, hypocenter	C₅×C₇×C₂₃	C₂×C₉
Frattini	C₃	C₃×D₈₀₅
Fitting	C₅×C₇×C₉×C₂₃	C₂
socle, cosocle	C₃×C₅×C₇×C₂₃	C₂×C₃
prime radical	C₃×D₈₀₅	C₃
LCS	G ▷ C₅×C₇×C₂₃
UCS	C₁ ◁ C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7245

Conjugacy classes & character table

3636 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×D₃₅, C₉×D₇×D₁₁₅, C₉×D₅×D₁₆₁, …
maximal normal subgroup of	C₉×D₂₃×D₃₅, C₉×D₇×D₁₁₅, C₉×D₅×D₁₆₁, …
maximal quotient of	C₉×Dic₈₀₅, C₂×C₉×D₈₀₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 9);