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C₉×D₅×D₁₈₁ #45656377

order	32580
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₅×D₁₈₁

Splittings

Fitting, Hall	C₅×C₉×C₁₈₁ ⋊ C₂²
derived, Hall	C₅×C₁₈₁ ⋊ C₂²×C₉
Hall	C₉×C₁₈₁ ⋊ C₂×D₅
Sylow	C₁₈₁ ⋊ C₂×C₉×D₅
Hall	C₅×C₉ ⋊ C₂×D₁₈₁
Sylow	C₅ ⋊ C₂×C₉×D₁₈₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅×D₁₈₁
commutator, hypocenter	C₅×C₁₈₁	C₂²×C₉
Frattini	C₃	C₃×D₅×D₁₈₁
Fitting	C₅×C₉×C₁₈₁	C₂²
socle, cosocle	C₃×C₅×C₁₈₁	C₂²×C₃
prime radical	C₃×D₅×D₁₈₁	C₃
LCS	G ▷ C₅×C₁₈₁
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 48);