Finite Group Databasebeta

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C₁₉×(C₃⋊D₃)⋊D₁₃ #22580372

order	8892
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×(C₃⋊D₃)⋊D₁₃
unambiguous semidirect product	(C₃⋊D₃)⋊(C₁₉×D₁₃)
unambiguous semidirect product	D₃₉⋊(D₃×C₁₉)

Splittings

Fitting, socle, Hall	C₃²×C₁₃×C₁₉ ⋊ C₂²
derived, Hall	C₃²×C₁₃ ⋊ C₂²×C₁₉
Hall	C₁₃×C₁₉ ⋊ D₃²
Hall	C₃²×C₁₉ ⋊ C₂×D₁₃
Sylow	C₁₃ ⋊ D₃²×C₁₉
Sylow	C₃² ⋊ C₂×C₁₉×D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	(C₃⋊D₃)⋊D₁₃
commutator, hypocenter	C₃²×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₁₉

88 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, 275);