Simplification of SUNF due to symmetry

[nmoynihan]

I am trying to simplify expressions involving FieldStrength and SUNF[I,j,k]. If I have an expression like:

Is there a way I can simplify this further, i.e. recognise that the symmetries of SUNF will simplify this expression?

Code, in case it is useful:

SUNF[i,j,k](FieldStrength[[Mu],[Nu],i]FieldStrength[[Nu],[Rho],j]FieldStrength[[Rho],[Mu],k] - FieldStrength[[Mu],[Nu],j]FieldStrength[[Nu],[Rho],i]FieldStrength[[Rho],[Mu],k])//SUNSimplify

[vsht]

Only by hand

exp = SUNF[i, j, 
   k] (FieldStrength[\[Mu], \[Nu], i] FieldStrength[\[Nu], \[Rho], 
      j] FieldStrength[\[Rho], \[Mu], k] - 
    FieldStrength[\[Mu], \[Nu], j] FieldStrength[\[Nu], \[Rho], 
      i] FieldStrength[\[Rho], \[Mu], k])

FS[a_, b_, c_] /; ! OrderedQ[{a, b}] := -FS[b, a, c];

exp /. FieldStrength[a_, b_, c_] :> 
  FS[LorentzIndex[a], LorentzIndex[b], SUNIndex[c]]
% // FCCanonicalizeDummyIndices

[nmoynihan]

Thanks!