Finite Group Databasebeta

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C₃×C₁₉×C₃⋊#261 #22580350

order	8892
isoclinism	isoclinic class of C₃⋊#261
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×C₃⋊#261
unambiguous semidirect product	C₃⋊(C₃×C₁₉×#261)

Splittings

Fitting, socle, Hall	C₃²×C₁₃×C₁₉ ⋊ C₄
derived	C₃×C₁₃ ⋊ C₃×C₄×C₁₉
Hall	C₁₃×C₁₉ ⋊ C₃×Dic₃
Hall	C₃²×C₁₉ ⋊ #261
Hall	C₃²×C₁₃ ⋊ C₄×C₁₉
Sylow	C₁₃ ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×#261

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₃×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₄
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 253);