Despite having direction and magnitude, angular displacement is not a vector because it does not obey the commutative law for addition. Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded and in this case commutativity appears.
dESpitE haViNG directioN And MagNitUDE, angular DIspLaCEMeNt is Not a vector becausE It dOeS not OBeY tHe cOMmutative law For aDDItIOn. nEvertHeleSs, WhEn dEalInG wIth iNfiNiTesiMal RotatIons, SecOnD order iNfinitesImalS can be diSCArded aNd in this CASe ComMUtAtIvity aPpears.