Finite Group Databasebeta

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C₂×D₃×C₁₉×C₁₃⋊C₃ #22580338

order	8892
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

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

Splittings

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

Subgroups

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

88 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, 241);