Finite Group Databasebeta

← Prev (#20301642) Next (#20301644) →

D₃×D₆₁₅ #20301643

order	7380
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₆₁₅
unambiguous semidirect product	(C₃×D₃)⋊D₂₀₅
unambiguous semidirect product	(C₅×D₃)⋊D₁₂₃
unambiguous semidirect product	(D₃×C₄₁)⋊D₁₅

Splittings

Fitting, socle, derived, Hall	C₃²×C₅×C₄₁ ⋊ C₂²
Hall	C₃²×C₄₁ ⋊ C₂×D₅
Hall	C₅×C₄₁ ⋊ D₃²
Hall	C₃²×C₅ ⋊ C₂×D₄₁
Sylow	C₄₁ ⋊ D₃×D₁₅
Sylow	C₃² ⋊ C₂×D₂₀₅
Sylow	C₅ ⋊ D₃×D₁₂₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₄₁	C₂²
LCS	G ▷ C₃²×C₅×C₄₁
UCS	C₁

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

927 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₃₀₇₅, D₃×C₃⋊(C₅⋊(D₄₁⋊C₅)), C₅×D₃×D₆₁₅, …
maximal normal subgroup of	D₃×C₃⋊(C₅⋊(D₄₁⋊C₅)), C₅×D₃×D₆₁₅
maximal quotient of	D₃×D₃₀₇₅, C₅×D₃×D₆₁₅, D₁₅×D₆₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 121);