Finite Group Databasebeta

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C₂×C₉×C₂₃×D₁₃ #24924499

order	10764
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₂₃×D₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₃	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₂₃
Frattini	C₃	C₂×C₃×C₂₃×D₁₃
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₂₃×D₁₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₂₃

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(10764, 35);