Catalyzes the NAD(+)-dependent oxidation of geraniol to geranial. Is involved in the anaerobic degradation of the monoterpene beta-myrcene. Can also catalyze the oxidation of (S)-perillyl alcohol to perillyl aldehyde, and to a lesser extent, the oxidation of nerol, citronellol, cumic alcohol, and benzyl alcohol. Cannot use NADP(+) instead of NAD(+) as cosubstrate. (2E)-geraniol + NAD(+) = (2E)-geranial + H(+) + NADH NAD(+) + perillyl alcohol = H(+) + NADH + perillyl aldehyde Binds 2 Zn(2+) ions per subunit. Is inhibited by EDTA, N-ethylmaleimide, diethylpyrocarbonate, and 1-cyclohexyl-N-(2-morpholinoethyl)carbodiimide in vitro. The values given here are for the native GeDH, the values for the recombinant protein can be found in another article (PubMed:22286981). Optimum pH is 9.4. Terpene metabolism; monoterpene degradation. Homodimer. By the monoterpene limonene. Belongs to the zinc-containing alcohol dehydrogenase family.