The First and Second Most Symmetric Nonsingular Cubic Surfaces
  The first and second most symmetric nonsingular cubic surfaces are x^3+y^3+z^3+t^3=0 and x^2y+y^2z+z^2t+t^2x=0, respectively. 
Hitoshi Kaneta, Stefano Marcugini, Fernanda Pambianco
math.AG