Finite Group Databasebeta

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C₂×C₉×D₂₉₉ #24924500

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

Aliases

direct product	C₂×C₉×D₂₉₉
unambiguous semidirect product	(C₂×C₂₃)⋊(C₉×D₁₃)

Splittings

Fitting	C₂×C₉×C₁₃×C₂₃ ⋊ C₂
derived, Hall	C₁₃×C₂₃ ⋊ C₂²×C₉
Hall	C₉×C₁₃×C₂₃ ⋊ C₂²
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	C₂×C₉	D₂₉₉
commutator, hypocenter	C₁₃×C₂₃	C₂²×C₉
Frattini	C₃	C₂×C₃×D₂₉₉
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
prime radical	C₂×C₃×D₂₉₉	C₃
cosocle	C₃×C₁₃×C₂₃	C₂²×C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2718 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 36);