Finite Group Databasebeta

← Prev (#20264199) Next (#20264201) →

D₃×D₅₃₃ #20264200

order	6396
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₅₃₃
unambiguous semidirect product	(D₃×C₁₃)⋊D₄₁
unambiguous semidirect product	(D₃×C₄₁)⋊D₁₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₃×C₄₁ ⋊ C₂²
Hall	C₁₃×C₄₁ ⋊ C₂×D₃
Hall	C₃×C₄₁ ⋊ C₂×D₁₃
Sylow	C₄₁ ⋊ D₃×D₁₃
Hall	C₃×C₁₃ ⋊ C₂×D₄₁
Sylow	C₁₃ ⋊ D₃×D₄₁
Sylow	C₃ ⋊ C₂×D₅₃₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₄₁	C₂²
LCS	G ▷ C₃×C₁₃×C₄₁
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

804 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₅₃₃, D₃×(C₁₃⋊C₃)⋊D₄₁, C₃×D₃×D₅₃₃, …
maximal normal subgroup of	D₃×(C₁₃⋊C₃)⋊D₄₁, C₃×D₃×D₅₃₃, D₃×C₁₃⋊(D₄₁⋊C₅), …
maximal quotient of	D₉×D₅₃₃, C₃×D₃×D₅₃₃, C₃⋊D₃×D₅₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 41);