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C₅×D₃×D₈ #91713

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

C₅×D₃×D₈

Splittings

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

Subgroups

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

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:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#3958, D₃×#3959, #11748281, …
maximal normal subgroup of	D₃×#3958, D₃×#3959, #11748281, …
maximal quotient of	C₅×#4756, C₅×#4759, C₅×#4760, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 789);