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C₉×D₁₀₈₅ #34086112

order	19530
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₀₈₅
unambiguous semidirect product	C₅⋊(C₉×D₂₁₇)

Splittings

Fitting, Hall	C₅×C₇×C₉×C₃₁ ⋊ C₂
derived, Hall	C₅×C₇×C₃₁ ⋊ C₂×C₉
Hall	C₇×C₉×C₃₁ ⋊ D₅
Hall	C₅×C₉×C₃₁ ⋊ D₇
Hall	C₅×C₇×C₉ ⋊ D₃₁
Hall	C₉×C₃₁ ⋊ D₃₅
Hall	C₇×C₃₁ ⋊ C₉×D₅
Hall	C₅×C₃₁ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₅₅
Hall	C₅×C₉ ⋊ D₂₁₇
Hall	C₅×C₇ ⋊ C₉×D₃₁
Sylow	C₃₁ ⋊ C₉×D₃₅
Sylow	C₇ ⋊ C₉×D₁₅₅
Sylow	C₅ ⋊ C₉×D₂₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₈₅
commutator, hypocenter	C₅×C₇×C₃₁	C₂×C₉
Frattini	C₃	C₃×D₁₀₈₅
Fitting	C₅×C₇×C₉×C₃₁	C₂
socle, cosocle	C₃×C₅×C₇×C₃₁	C₂×C₃
prime radical	C₃×D₁₀₈₅	C₃
LCS	G ▷ C₅×C₇×C₃₁
UCS	C₁ ◁ C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9765

Conjugacy classes & character table

4896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 17);