Finite Group Databasebeta

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C₂×C₉×C₁₉×D₂₃ #30628566

order	15732
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×C₁₉×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂²×C₉×C₁₉)
unambiguous semidirect product	(C₂×C₂₃)⋊(C₂×C₉×C₁₉)

Splittings

Fitting	C₂×C₉×C₁₉×C₂₃ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂²×C₉×C₁₉
Hall	C₉×C₁₉×C₂₃ ⋊ C₂²
Hall	C₁₉×C₂₃ ⋊ C₂²×C₉
Hall	C₉×C₂₃ ⋊ C₂²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₂₃
commutator, hypocenter	C₂₃	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×D₂₃
Fitting	C₂×C₉×C₁₉×C₂₃	C₂
socle	C₂×C₃×C₁₉×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₁₉×D₂₃	C₃
cosocle	C₃×C₂₃	C₂²×C₃×C₁₉
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₉×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7866

Conjugacy classes & character table

4446 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 28);