  We have synthesized Sr$_6$Co$_5$O$_{15}$, a quasi-one-dimensional oxide,
measured its magnetic properties and calculated its electronic structure by ab
initio techniques. We have found strong evidence for its electronic and
magnetic behavior not to follow the trend of its structural series. The
magnetic coupling inside the CoO$_3$ chains is not purely ferromagnetic, the
long-range coupling inside them is very weak. The Co moments are slightly
canted due to their large orbital angular momenta being oriented along each
particular quantization axis, that is different for each Co$^{4+}$ atom in the
structure. Our thermopower calculations are in agreement with the experiment,
supporting our model of the magnetic ground state of the compound.
