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D₃×D₄₀ #91252

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₃×D₄₀

Splittings

Fitting	C₃×C₅×C₈ ⋊ C₂²
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₅ ⋊ D₃×D₈
Sylow	C₃ ⋊ C₂×D₄₀

Subgroups

	subgroup	G/H
center	C₂	D₃×D₂₀
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2,4,5,3)(6,7,11,13,9,12,8,10)(14,15,16);(2,3)(4,5)(7,10)(8,11)(12,13);(15,16)

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₈₀, D₃×#3932, #11746820, …
maximal normal subgroup of	D₃×D₈₀, D₃×#3932, #11746820, …
maximal quotient of	D₃×D₈₀, D₃×#3932, #11746820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 328);