Finite Group Databasebeta

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C₉×C₁₃×D₆₅ #29503596

order	15210
isoclinism	isoclinic class of D₆₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₃×D₆₅
unambiguous semidirect product	C₅⋊(C₉×C₁₃×D₁₃)

Splittings

Fitting, Hall	C₅×C₉×C₁₃² ⋊ C₂
derived	C₅×C₁₃ ⋊ C₂×C₉×C₁₃
Hall	C₉×C₁₃² ⋊ D₅
Hall	C₅×C₁₃² ⋊ C₂×C₉
Sylow	C₁₃² ⋊ C₉×D₅
Hall	C₅×C₉ ⋊ C₁₃×D₁₃
Sylow	C₅ ⋊ C₉×C₁₃×D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃	D₆₅
commutator, hypocenter	C₅×C₁₃	C₂×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×D₆₅
Fitting	C₅×C₉×C₁₃²	C₂
socle	C₃×C₅×C₁₃²	C₂×C₃
prime radical	C₃×C₁₃×D₆₅	C₃
cosocle	C₃×C₅×C₁₃	C₂×C₃×C₁₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₉×C₁₃

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1170

Conjugacy classes & character table

3978 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₃×#63122, C₉×C₁₃×#63121, C₉×#16810005, …
maximal normal subgroup of	C₉×C₁₃×#63122, C₉×C₁₃×#63121, C₉×#16810005, …
maximal quotient of	C₉×C₁₃×Dic₆₅, C₂×C₉×C₁₃×D₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 59);