Because they are fermions the anti-commutators of the Jordan algebra become commutators. It is known that E 6 has subgroup O(10) and so is big enough to include the Standard Model. An E 8 gauge group, for example, would have 8 neutral bosons, 120 charged bosons and 120 charged anti-bosons. To account for the 248 fermions in the lowest multiplet of E 8, these would either have to include anti-particles (and so have baryogenesis), have new undiscovered particles, or have gravity-like (spin connection) bosons affecting elements of the particles spin direction. Each of these possesses theoretical problems.