  The magnetic and electrical properties of Co$_3$TeO$_6$ single-crystals with
corundum related structure reveal a magnetic-field induced polarization below
21 K. A sharp peak in the specific heat at \approx 18 K indicates a
reconstructive-type first-order phase transition. From second-harmonic
generation (SHG) measurements breaking of inversion symmetry is evident and the
point-group symmetry was determined as m. The temperature and magnetic-field
dependence of the magnetic and electrical polarizations are discussed in the
light of the SHG results.
