As is well known Minkowski spacetime (which is four dimensional vector space with scalar product $\eta \_{\mu \nu}$ of signature $-+++$) is maximally symmetric, which manifests itself in presence of ten Killing vector fields. Those are generators of one parameter groups of isometries, which can be understood as translations, boosts (hyperbolic rotations) and Euclidean rotations. There are also five conformal Killing vectors fields, which are generators of one parameter groups of conformal transformations. One of those transformations is simply scaling whole space. However there are four others, with generators:

$K \_ {\mu} = 2 \eta \_{\mu \alpha} x^{\alpha} x^{\nu} \partial \_{\nu} - x^{\alpha} x\_{\alpha} \partial \_{\mu}$

With standard identification of tangent vectors and partial derivatives understood in this formula. My question is what are those transformations? Can I visualize them or explicitly find those groups? What is their interpretation or significance? Any insight will be appreciated.