Sam: No, it’s Shittas Beis Hillel (and how we pasken, though Rabbeinu Gershom changed things a bit for Ashkenazim.) Beis Shammai is more machmir when he may divorce her (i.e. for immorality not for simply burning his food), but we don’t pasken like B”S. (Nor do we pasken like Rebbi Akiva who says he may divorce her if he found a prettier woman or like R. Meir who holds that if a woman ate, walked haughtily, or nursed a baby in the market, her husband must divorce her.)
The Achronim go back and forth whether its dealing with a zivug rishon or sheini. They essentially say one should be much more reluctant to divorce a zivug rishon, although strictly according to halacha he may do so for a small reason, though it is very discouraged.
Shulchan Aruch paskens that if a woman is not modest like proper Bnos Yisrael, it is a Mitzvah to divorce her.