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C₂₃×Dic₁₃⋊C₉ #24924467

order	10764
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₂₃)
unambiguous semidirect product	(C₂₃×Dic₁₃)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₂₃
Hall	C₂₃×C₁₃⋊C₉ ⋊ C₄
Hall	C₂₃×Dic₁₃ ⋊ C₉
Hall	C₁₃×C₂₃ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₂₃
Hall	Dic₁₃ ⋊ C₉×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₂₃
Frattini	C₂×C₃	C₂₃×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₃	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₂₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 3);