Finite Group Databasebeta

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C₂²×C₂₃×C₁₃⋊C₉ #24924495

order	10764
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₂₃×C₁₃⋊C₉

Splittings

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

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 31);