The chemical formula for detergent certainly is not "c3h8o5," as was suggested. ("c3h8o5" does not even exist as a molecule.)

Rather, the chemical formula for "detergent" really depends on what you mean by the word. By itself the word does not connoted any specific formula (must/must not have this function group).

Commercial detergents are made up of many different chemical compounds (different surfactants, colorants, pH modifiers, chlorinated and non-chlorinated whiteners, etc). For example, one effective (albeit harsh) surfactant is sodium lauryl sulfate (aka sodium dodecyl sulfate): C12H25NaO4S.