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D₃×D₅₈₉ #20296643

order	7068
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₅₈₉
unambiguous semidirect product	(D₃×C₁₉)⋊D₃₁
unambiguous semidirect product	(D₃×C₃₁)⋊D₁₉

Splittings

Fitting, socle, derived, Hall	C₃×C₁₉×C₃₁ ⋊ C₂²
Hall	C₁₉×C₃₁ ⋊ C₂×D₃
Hall	C₃×C₃₁ ⋊ C₂×D₁₉
Hall	C₃×C₁₉ ⋊ C₂×D₃₁
Sylow	C₃₁ ⋊ D₃×D₁₉
Sylow	C₁₉ ⋊ D₃×D₃₁
Sylow	C₃ ⋊ C₂×D₅₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₉×C₃₁	C₂²
LCS	G ▷ C₃×C₁₉×C₃₁
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

888 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₅₈₉, D₃×#16812976, D₃×#16812975, …
maximal normal subgroup of	D₃×#16812976, D₃×#16812975, D₃×(C₁₉⋊C₃)⋊D₃₁, …
maximal quotient of	D₉×D₅₈₉, C₃×D₃×D₅₈₉, D₃×D₁₇₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7068, 47);