The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D2h point group<br/>symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C2h molecules in terms of the nine independent second rank orientational order parameters defining the C2h biaxial nematic. In addition there is a rank one order parameter constructed from two pseudovectors which is only non-zero in the C2h phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behaviour is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points
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