Finite Group Databasebeta

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C₉×C₁₉×Dic₂₃ #30628541

order	15732
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×Dic₂₃
unambiguous semidirect product	C₂₃⋊(C₄×C₉×C₁₉)

Splittings

derived, Sylow	C₂₃ ⋊ C₄×C₉×C₁₉
Hall	C₉×C₁₉×C₂₃ ⋊ C₄
Hall	C₁₉×C₂₃ ⋊ C₄×C₉
Hall	C₉×C₂₃ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₂₃
commutator, hypocenter	C₂₃	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₃×C₁₉×D₂₃
Fitting	C₂×C₉×C₁₉×C₂₃	C₂
socle, prime radical	C₂×C₃×C₁₉×C₂₃	C₂×C₃
cosocle	C₂×C₃×C₂₃	C₂×C₃×C₁₉
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₉×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15732

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, 3);