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C₉×D₆₃₁ #26015481

order	11358
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₆₃₁

Splittings

Fitting, Hall	C₉×C₆₃₁ ⋊ C₂
derived, Sylow	C₆₃₁ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₆₃₁
commutator, hypocenter	C₆₃₁	C₂×C₉
Frattini	C₃	C₃×D₆₃₁
Fitting	C₉×C₆₃₁	C₂
socle, cosocle	C₃×C₆₃₁	C₂×C₃
prime radical	C₃×D₆₃₁	C₃
LCS	G ▷ C₆₃₁
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2853 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×D₆₃₁, C₂×C₉×D₆₃₁
maximal normal subgroup of	D₉×D₆₃₁, C₂×C₉×D₆₃₁
maximal quotient of	C₉×Dic₆₃₁, C₂×C₉×D₆₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11358, 5);