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C₉×D₁₃×D₂₃ #24924486

order	10764
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₃×D₂₃

Splittings

Fitting, Hall	C₉×C₁₃×C₂₃ ⋊ C₂²
derived, Hall	C₁₃×C₂₃ ⋊ C₂²×C₉
Hall	C₉×C₂₃ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₂₃
Sylow	C₂₃ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₂₃
commutator, hypocenter	C₁₃×C₂₃	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₂₃
Fitting	C₉×C₁₃×C₂₃	C₂²
socle, cosocle	C₃×C₁₃×C₂₃	C₂²×C₃
prime radical	C₃×D₁₃×D₂₃	C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

936 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 22);