Finite Group Databasebeta

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D₅×C₁₉×C₁₆₉ #44545764

order	32110
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₁₆₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₁₉×C₁₆₉
unambiguous semidirect product	C₅⋊(C₂×C₁₉×C₁₆₉)

Splittings

Fitting, Hall	C₅×C₁₉×C₁₆₉ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₁₉×C₁₆₉
Hall	C₅×C₁₆₉ ⋊ C₂×C₁₉
Hall	C₅×C₁₉ ⋊ C₂×C₁₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₁₆₉	D₅
commutator, hypocenter	C₅	C₂×C₁₉×C₁₆₉
Frattini	C₁₃	D₅×C₁₃×C₁₉
Fitting	C₅×C₁₉×C₁₆₉	C₂
socle	C₅×C₁₃×C₁₉	C₂×C₁₃
prime radical	D₅×C₁₃×C₁₉	C₁₃
cosocle	C₅×C₁₃	C₂×C₁₃×C₁₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₉×C₁₆₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16055

Conjugacy classes & character table

12844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32110, 5);