Catalyzes the oxidation of primary alcohols including methanol. a primary alcohol + 2 Fe(III)-[cytochrome cL] = an aldehyde + 2 Fe(II)-[cytochrome cL] + 2 H(+) Binds 1 PQQ group per subunit. PQQ is inserted between disulfide Cys-130-Cys-131 and the indole ring of Trp-270. Binds 1 Ca(2+) ion per subunit. Heterotetramer composed of 2 alpha and 2 beta subunits. Periplasmic, but associated with inner membrane. Belongs to the bacterial PQQ dehydrogenase family.