To make OAT Great Sword (Fulgurante), you need to start out with a Break Blade.
"Break Blade" supports PLD/DRK/RUN. Fulgurante supports PLD/DRK.

I happen to have a OAT Fulgurante.
People in Jeuno, says the Elemental trial GS supports RUN, though.

How can you loose support for a Job during somewhere in the trial stages? Isn't that wierd? I want Fulgurante on RUN ; ;