Finite Group Databasebeta

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C₂×C₃×D₄₀ #91620

order	480
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₃×D₄₀

Splittings

Fitting	C₂×C₃×C₅×C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₅ ⋊ C₂×C₃×D₈

Subgroups

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

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

(3,4,5)(6,7,9,10,8)(11,12,16,18,14,17,13,15);(1,2)(7,8)(9,10)(12,15)(13,16)(17,18);(1,2)

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745891, #11745892, #11745915, …
maximal normal subgroup of	#11745891, #11745892, #11745915, …
maximal quotient of	C₃×#64971, C₃×C₄×D₄₀, C₃×#64983, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 696);