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C₉×D₆₀₁ #24925241

order	10818
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₆₀₁

Splittings

Fitting, Hall	C₉×C₆₀₁ ⋊ C₂
derived, Sylow	C₆₀₁ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₆₀₁
commutator, hypocenter	C₆₀₁	C₂×C₉
Frattini	C₃	C₃×D₆₀₁
Fitting	C₉×C₆₀₁	C₂
socle, cosocle	C₃×C₆₀₁	C₂×C₃
prime radical	C₃×D₆₀₁	C₃
LCS	G ▷ C₆₀₁
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2718 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#14558894, C₉⋊#14558894, D₉×D₆₀₁, …
maximal normal subgroup of	C₉×#14558894, C₉⋊#14558894, D₉×D₆₀₁, …
maximal quotient of	C₉×Dic₆₀₁, C₂×C₉×D₆₀₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10818, 5);