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C₂×C₉×D₉₀₅ #45656397

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

Aliases

direct product	C₂×C₉×D₉₀₅
unambiguous semidirect product	(C₂×C₅)⋊(C₉×D₁₈₁)

Splittings

Fitting	C₂×C₅×C₉×C₁₈₁ ⋊ C₂
derived, Hall	C₅×C₁₈₁ ⋊ C₂²×C₉
Hall	C₅×C₉×C₁₈₁ ⋊ C₂²
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	C₂×C₉	D₉₀₅
commutator, hypocenter	C₅×C₁₈₁	C₂²×C₉
Frattini	C₃	C₂×C₃×D₉₀₅
Fitting	C₂×C₅×C₉×C₁₈₁	C₂
socle	C₂×C₃×C₅×C₁₈₁	C₂×C₃
prime radical	C₂×C₃×D₉₀₅	C₃
cosocle	C₃×C₅×C₁₈₁	C₂²×C₃
LCS	G ▷ C₅×C₁₈₁
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 68);