Permutating rhymes with:
agitating, debilitating, devastating, dictating, facilitating, gravitating, hesitating, imitating, incapacitating, irritating, levitating, meditating, necessitating, overstating, precipitating, rehabilitating, resuscitating, rotating, understating
Permutating sounds like:
parenting, permeating, permitting, permutations, premonitions, prentnieks, printing, printing's, printings, promoting, promotions