  We introduce the probabilistic symbol for the class of homogeneous diffusions
with jumps (in the sense of Jacod/Shiryaev). This concept generalizes the
well-known characteristic exponent of a L\'{e}vy process. Using the symbol, we
introduce eight indices which generalize the Blumenthal-Getoor index $\beta$
and the Pruitt index $\delta$. These indices are used afterwards to obtain
growth and H\"{o}lder conditions of the process. In the future, the technical
main results will be used to derive further fine properties. Since virtually
all examples of homogeneous diffusions in the literature are Markovian, we
construct a process which does not have this property.
