Finite Group Databasebeta

← Prev (#32912471) Next (#32912473) →

C₉×D₁₀₁₅ #32912472

order	18270
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₀₁₅
unambiguous semidirect product	C₅⋊(C₉×D₂₀₃)
unambiguous semidirect product	C₂₉⋊(C₉×D₃₅)

Splittings

Fitting, Hall	C₅×C₇×C₉×C₂₉ ⋊ C₂
derived, Hall	C₅×C₇×C₂₉ ⋊ C₂×C₉
Hall	C₇×C₉×C₂₉ ⋊ D₅
Hall	C₅×C₉×C₂₉ ⋊ D₇
Hall	C₅×C₇×C₉ ⋊ D₂₉
Hall	C₉×C₂₉ ⋊ D₃₅
Hall	C₇×C₂₉ ⋊ C₉×D₅
Hall	C₅×C₂₉ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₄₅
Hall	C₅×C₉ ⋊ D₂₀₃
Hall	C₅×C₇ ⋊ C₉×D₂₉
Sylow	C₂₉ ⋊ C₉×D₃₅
Sylow	C₇ ⋊ C₉×D₁₄₅
Sylow	C₅ ⋊ C₉×D₂₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₁₅
commutator, hypocenter	C₅×C₇×C₂₉	C₂×C₉
Frattini	C₃	C₃×D₁₀₁₅
Fitting	C₅×C₇×C₉×C₂₉	C₂
socle, cosocle	C₃×C₅×C₇×C₂₉	C₂×C₃
prime radical	C₃×D₁₀₁₅	C₃
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9135

Conjugacy classes & character table

4581 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₉×D₃₅, C₉×D₇×D₁₄₅, C₉×D₅×D₂₀₃, …
maximal normal subgroup of	C₉×D₂₉×D₃₅, C₉×D₇×D₁₄₅, C₉×D₅×D₂₀₃, …
maximal quotient of	C₉×Dic₁₀₁₅, C₂×C₉×D₁₀₁₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 10);