Consider a finite collection of elements of the rotation group SO(3). We are interested in measuring to which extent this collection of points is «well distributed».

A natural approach to this problem is to compute the energy of the sequence, thought of as some kind of electrical potential, and to compare the result with the minimum posible value. In this paper we compute sharp upper and lower bounds for the minimal energy of a finite collection of elements of SO(3) for two different choices of the energy: the Green energy and the Riesz 3-energy. We also provide simple formulas for the Green energy in the rotation group and other useful expresions.