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C₂×D₂₃×C₁₃⋊C₉ #24924483

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

Aliases

direct product	C₂×D₂₃×C₁₃⋊C₉
unambiguous semidirect product	C₂₃⋊(C₂²×C₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₂₃)⋊(C₂×C₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₁₃×D₂₃)⋊C₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊C₃×D₂₃
commutator, hypocenter	C₁₃×C₂₃	C₂²×C₉
Frattini	C₃	C₂×C₁₃⋊C₃×D₂₃
Fitting, socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₁₃×D₂₃	C₃
cosocle	C₃×C₁₃×C₂₃	C₂²×C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 19);