Finite Group Databasebeta

← Prev (#91925) Next (#91927) →

C₂×D₃×#170 #91926

order	480
isoclinism	isoclinic class of D₃×AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₃×#170

Splittings

derived, Hall	C₃×C₅ ⋊ C₂²×C₈
Sylow	C₅ ⋊ C₂×D₃×C₈
Sylow	C₃ ⋊ C₂²×#170

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₂²×C₈
Frattini	C₂	C₂×D₃×AGL(1,𝔽₅)
Fitting, socle	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×C₅×D₃	C₄
cosocle	C₃×Dic₅	C₂³
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×D₃×#170, D₁₂×#170, D₃×C₄⋊#170, …
maximal normal subgroup of	C₄×D₃×#170, D₁₂×#170, D₃×C₄⋊#170, …
maximal quotient of	C₂×D₃×#674, #11751736, D₃×#3998, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1002);