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C₅×C₉×D₆₅ #19154336

order	5850
isoclinism	isoclinic class of D₆₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

Fitting, Hall	C₅²×C₉×C₁₃ ⋊ C₂
derived	C₅×C₁₃ ⋊ C₂×C₅×C₉
Hall	C₅²×C₁₃ ⋊ C₂×C₉
Hall	C₅²×C₉ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ C₅×D₅
Sylow	C₅² ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₅×C₉×D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₆₅
commutator, hypocenter	C₅×C₁₃	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₆₅
Fitting	C₅²×C₉×C₁₃	C₂
socle	C₃×C₅²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₅×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×#63122, C₅×C₉×#63121, C₅×C₉×D₅×D₁₃, …
maximal normal subgroup of	C₅×C₉×#63122, C₅×C₉×#63121, C₅×C₉×D₅×D₁₃, …
maximal quotient of	C₅×C₉×Dic₆₅, C₂×C₅×C₉×D₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 52);