Finite Group Databasebeta

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C₁₃×C₁₉×Dic₂₃ #36384335

order	22724
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉×Dic₂₃
unambiguous semidirect product	C₂₃⋊(C₄×C₁₃×C₁₉)

Splittings

derived, Sylow	C₂₃ ⋊ C₄×C₁₃×C₁₉
Hall	C₁₃×C₁₉×C₂₃ ⋊ C₄
Hall	C₁₉×C₂₃ ⋊ C₄×C₁₃
Hall	C₁₃×C₂₃ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₂₃
commutator, hypocenter	C₂₃	C₄×C₁₃×C₁₉
Frattini	C₂	C₁₃×C₁₉×D₂₃
Fitting, socle, prime radical	C₂×C₁₃×C₁₉×C₂₃	C₂
cosocle	C₂×C₂₃	C₂×C₁₃×C₁₉
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₁₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22724

Conjugacy classes & character table

6422 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22724, 2);