Finite Group Databasebeta

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C₂×D₃×C₁₃×C₁₉⋊C₃ #22580331

order	8892
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₁₃×C₁₉⋊C₃
unambiguous semidirect product	C₃⋊(C₂²×C₁₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₁₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×D₃×C₁₉)⋊(C₃×C₁₃)

Splittings

Fitting, socle	C₂×C₃×C₁₃×C₁₉ ⋊ C₂×C₃
derived	C₃×C₁₉ ⋊ C₂²×C₃×C₁₃
Hall	C₃×C₁₃×C₁₉⋊C₃ ⋊ C₂²
Hall	C₁₃×C₁₉ ⋊ C₂×C₃×D₃
Hall	C₃×C₁₉⋊C₃ ⋊ C₂²×C₁₃
Sylow	C₁₉ ⋊ C₂×C₃×D₃×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₃×C₁₉⋊C₃
commutator, hypocenter	C₃×C₁₉	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₁₃

88 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, 234);