Finite Group Databasebeta

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D₃×C₁₃×D₅₇ #22580366

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

Aliases

direct product	D₃×C₁₃×D₅₇
unambiguous semidirect product	(C₃×D₃)⋊(C₁₃×D₁₉)
unambiguous semidirect product	(D₃×C₁₉)⋊(D₃×C₁₃)

Splittings

Fitting, socle, Hall	C₃²×C₁₃×C₁₉ ⋊ C₂²
derived, Hall	C₃²×C₁₉ ⋊ C₂²×C₁₃
Hall	C₁₃×C₁₉ ⋊ D₃²
Hall	C₃²×C₁₃ ⋊ C₂×D₁₉
Sylow	C₁₉ ⋊ D₃²×C₁₃
Sylow	C₃² ⋊ C₂×C₁₃×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₅₇
commutator, hypocenter	C₃²×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₁₃

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 269);