C₃×#687 #6684

order	240
isoclinism	isoclinic class of #686
automorphism	Aut(G) = C₂²×D₄×AGL(1,𝔽₅) (order 640) · Inn(G) = C₂²⋊D₅ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₅ ⋊ SD₁₆
Sylow	C₅ ⋊ C₃×SD₁₆

40 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 45);