Finite Group Databasebeta

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C₃×Dic₃×C₁₉×C₂₉ #34090641

order	19836
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₃×C₁₉×C₂₉
unambiguous semidirect product	C₃⋊(C₃×C₄×C₁₉×C₂₉)

Splittings

derived	C₃ ⋊ C₃×C₄×C₁₉×C₂₉
Hall	C₃²×C₁₉×C₂₉ ⋊ C₄
Hall	C₃²×C₂₉ ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ C₄×C₂₉
Sylow	C₃² ⋊ C₄×C₁₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉×C₂₉	D₃
commutator, hypocenter	C₃	C₃×C₄×C₁₉×C₂₉
Frattini	C₂	C₃×D₃×C₁₉×C₂₉
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₂₉	C₂
cosocle	C₂×C₃	C₂×C₃×C₁₉×C₂₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₉×C₂₉

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6612

Conjugacy classes & character table

9918 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 57);