  We characterize inter- and intraisotope interorbital interactions between
atoms in the 1S0 ground state and the 3P0 metastable state in interacting
Fermi-Fermi mixtures of 171Yb and 173Yb. We perform high-precision clock
spectroscopy to measure interaction-induced energy shifts in a deep 3D optical
lattice and determine the corresponding scattering lengths. We find the elastic
interaction of the interisotope mixtures 173Yb_e-171Yb_g and 173Yb_g-171Yb_e to
be weakly attractive and very similar, while the corresponding two-body loss
coefficients differ by more than two orders of magnitude. By comparing
different spin mixtures we experimentally demonstrate the SU(2)xSU(6) symmetry
of all elastic and inelastic interactions. Furthermore, we measure the
spin-exchange interaction in 171Yb and confirm its previously observed
antiferromagnetic nature.
