  From a recent paper, we recall the Hopf monoid structure on the
supercharacters of the unipotent uppertriangular groups over a finite field. We
give cancelation free formula for the antipode applied to the bases of class
functions and power sum functions, giving new cancelation free formulae for the
standard Hopf algebra of supercharacters and symmetric functions in
noncommuting variables. We also give partial results for the antipode on the
supercharacter basis, and explicitly describe the primitives of this Hopf
monoid.
