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D₃×D₄₆₅ #19150161

order	5580
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₄₆₅
unambiguous semidirect product	(C₃×D₃)⋊D₁₅₅
unambiguous semidirect product	(C₅×D₃)⋊D₉₃
unambiguous semidirect product	(D₃×C₃₁)⋊D₁₅

Splittings

Fitting, socle, derived, Hall	C₃²×C₅×C₃₁ ⋊ C₂²
Hall	C₃²×C₃₁ ⋊ C₂×D₅
Hall	C₅×C₃₁ ⋊ D₃²
Hall	C₃²×C₅ ⋊ C₂×D₃₁
Sylow	C₃₁ ⋊ D₃×D₁₅
Sylow	C₃² ⋊ C₂×D₁₅₅
Sylow	C₅ ⋊ D₃×D₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₃₁	C₂²
LCS	G ▷ C₃²×C₅×C₃₁
UCS	C₁

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

702 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₂₃₂₅, D₃×C₃⋊(C₅⋊(D₃₁⋊C₅)), C₅×D₃×D₄₆₅, …
maximal normal subgroup of	D₃×C₃⋊(C₅⋊(D₃₁⋊C₅)), C₅×D₃×D₄₆₅
maximal quotient of	D₃×D₂₃₂₅, C₅×D₃×D₄₆₅, D₁₅×D₄₆₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 150);