Monopole charges for arbitrary compact gauge groups and Higgs fields in any representation

The topological invariants of monopoles are described for an arbitrary compact gauge group G and Higgs field PHI in any representation. The results generalize those obtained recently for compact and simply connected G and PHI in the adjoint representation. The cases when the residual symmetry group is H=U(1) or H=U(3) are worked out explicitly. This latter is needed to accomodate fractional electric charge with monopoles having one Dirac unit magnetic charge. The general theory is illustrated on the SU(5) monopole