Finite Group Databasebeta

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C₁₉×C₂₃×Dic₉ #30628544

order	15732
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₂₃×Dic₉
unambiguous semidirect product	C₉⋊(C₄×C₁₉×C₂₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₃	D₉
commutator, hypocenter	C₉	C₄×C₁₉×C₂₃
Frattini	C₂×C₃	D₃×C₁₉×C₂₃
Fitting	C₂×C₉×C₁₉×C₂₃	C₂
socle, prime radical	C₂×C₃×C₁₉×C₂₃	D₃
cosocle	C₂×C₉	C₂×C₁₉×C₂₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₂₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15732

Conjugacy classes & character table

5244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 6);