In this paper, we present a construction for the compact form of the exceptional Lie group by exponentiating the corresponding Lie algebra , which we realize as the sum of , the derivations of the exceptional Jordan algebra of dimension 3 with octonionic entries, and the right multiplication by the elements of with vanishing trace. Our parametrization is a generalization of the Euler angles for SU(2) and it is based on the fibration of via an subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for . An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the group manifold.
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