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C₉×D₁₄₃₅ #38788907

order	25830
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₄₃₅
unambiguous semidirect product	C₅⋊(C₉×D₂₈₇)
unambiguous semidirect product	C₄₁⋊(C₉×D₃₅)

Splittings

Fitting, Hall	C₅×C₇×C₉×C₄₁ ⋊ C₂
derived, Hall	C₅×C₇×C₄₁ ⋊ C₂×C₉
Hall	C₇×C₉×C₄₁ ⋊ D₅
Hall	C₅×C₉×C₄₁ ⋊ D₇
Hall	C₉×C₄₁ ⋊ D₃₅
Hall	C₅×C₇×C₉ ⋊ D₄₁
Hall	C₇×C₄₁ ⋊ C₉×D₅
Hall	C₅×C₄₁ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₂₀₅
Hall	C₅×C₉ ⋊ D₂₈₇
Sylow	C₄₁ ⋊ C₉×D₃₅
Hall	C₅×C₇ ⋊ C₉×D₄₁
Sylow	C₇ ⋊ C₉×D₂₀₅
Sylow	C₅ ⋊ C₉×D₂₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₄₃₅
commutator, hypocenter	C₅×C₇×C₄₁	C₂×C₉
Frattini	C₃	C₃×D₁₄₃₅
Fitting	C₅×C₇×C₉×C₄₁	C₂
socle, cosocle	C₃×C₅×C₇×C₄₁	C₂×C₃
prime radical	C₃×D₁₄₃₅	C₃
LCS	G ▷ C₅×C₇×C₄₁
UCS	C₁ ◁ C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12915

Conjugacy classes & character table

6471 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 11);