Finite Group Databasebeta

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Dic₃×C₁₃×C₁₉⋊C₃ #22580204

order	8892
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

702 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 107);