Exceptional Lie groups hierarchy, orthogonal and unitary groups in connection with symmetries of E-infinity space-time

In the present work, different derivations of the 548 isometries of E-infinity symmetry group are presented. The connection between the dimensions of exceptional Lie groups, orthogonal, unitary groups and the 548 is found. The work gives some arguments for deriving the inverse electromagnetic fine structure constant from 1152 bosons and an equal number of fermions following the light cone quantization of the GS action of a super Maxwell theory.