C₃×#683 #6680

order	240
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂⁵×AGL(1,𝔽₅) (order 640) · Inn(G) = C₂×D₅ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₅ ⋊ C₄⋊C₄
Sylow	C₅ ⋊ C₃×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 240

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 41);