Finite Group Databasebeta

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Dic₃×C₁₉×C₁₃⋊C₃ #22580211

order	8892
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

derived	C₃×C₁₃ ⋊ C₃×C₄×C₁₉
Hall	C₃×C₁₉×C₁₃⋊C₃ ⋊ C₄
Hall	C₁₃×C₁₉ ⋊ C₃×Dic₃
Hall	C₃×C₁₃⋊C₃ ⋊ C₄×C₁₉
Sylow	C₁₃ ⋊ C₃×Dic₃×C₁₉

Subgroups

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

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

798 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 114);