C₃×C₄×C₅ #303

order	60
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄ (order 16) · Inn(G) = C₁ · Out(G) = C₂²×C₄
holomorph	G ⋊ Aut(G) = D₃×D₄×AGL(1,𝔽₅)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 1 generator on 12 points:

(1,2,3,4)(5,6,7)(8,9,10,11,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(60, 4);