Finite Group Databasebeta

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C₃×C₁₉×AGL(1,𝔽₁₃) #22580259

order	8892
isoclinism	isoclinic class of AGL(1,𝔽₁₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉×AGL(1,𝔽₁₃)
unambiguous semidirect product	#261⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×#261)⋊(C₃×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃	C₃²×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₃×C₄
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

741 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 162);