Finite Group Databasebeta

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C₃×Dic₃×C₁₃×C₁₉ #22580226

order	8892
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₃×C₁₃×C₁₉
unambiguous semidirect product	C₃⋊(C₃×C₄×C₁₃×C₁₉)

Splittings

derived	C₃ ⋊ C₃×C₄×C₁₃×C₁₉
Hall	C₃²×C₁₃×C₁₉ ⋊ C₄
Hall	C₃²×C₁₉ ⋊ C₄×C₁₃
Hall	C₃²×C₁₃ ⋊ C₄×C₁₉
Sylow	C₃² ⋊ C₄×C₁₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃×C₁₉	D₃
commutator, hypocenter	C₃	C₃×C₄×C₁₃×C₁₉
Frattini	C₂	C₃×D₃×C₁₃×C₁₉
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

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(8892, 129);