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In critical dimensions these spacetimes admit extensions with twistorial coordinates plus a dilatonic coordinate to causal spacetimes coordinatized by Jordan algebras $J_3^{A}$ of degree three over the four division algebras $A= R , C , H , O $. We study the minimal unitary representation (minrep) of the conformal group $E_{7(-25)}$ of the spacetime coordinatized by the exceptional Jordan algebra $J_3^{O}$. 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In critical dimensions these spacetimes admit extensions with twistorial coordinates plus a dilatonic coordinate to causal spacetimes coordinatized by Jordan algebras $J_3^{A}$ of degree three over the four division algebras $A= R , C , H , O $. We study the minimal unitary representation (minrep) of the conformal group $E_{7(-25)}$ of the spacetime coordinatized by the exceptional Jordan algebra $J_3^{O}$. 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