Finite Group Databasebeta

← Prev (#24924481) Next (#24924483) →

C₂×C₂₃⋊(D₁₃⋊C₉) #24924482

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

Aliases

direct product	C₂×C₂₃⋊(D₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₂₃)⋊(D₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₁₃⋊C₉)⋊D₂₃
unambiguous semidirect product	(C₂×D₂₉₉)⋊C₉

Splittings

derived, Hall	C₁₃×C₂₃ ⋊ C₂²×C₉
Hall	C₂₃×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×D₂₉₉ ⋊ C₉
Hall	C₁₃⋊C₉ ⋊ C₂×D₂₃
Sylow	C₂₃ ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×C₉×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂₃⋊(D₁₃⋊C₃)
commutator, hypocenter	C₁₃×C₂₃	C₂²×C₉
Frattini	C₃	C₂×C₂₃⋊(D₁₃⋊C₃)
Fitting, 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×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

510 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 18);