SO(2N)grand unification in anSU(N)basis

We discuss the algebra and the representations of $\mathrm{SO}\mathrm{}\left(2N\right)\mathrm{}$ groups used in the construction of grand unified theories in a basis in which its connections with the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ grand unification is most transparent. Specializing to the case of $N=5\mathrm{}$, we discuss the problem of fermion masses for various Higgs representations. Applying our considerations to SO(12) grand unification, we comment on the nature of weak interactions of the extra generation of fermions present in the 32-dimensional spinor representation of this group.