Inverse permutation index
Mathematica, 74 bytes
Max@k[i,Flatten@Outer[i=Permutations[j=Range@#];k=Position,{i[[#]]},j,1]]&amp;

Uses 1-indexing. Very inefficient. (uses ~11GB of memory when the input is 11)
Explanation
j=Range@#

Generate a list from 1 to N. Store that in j.
i=Permutations[...]

Find all permutations of j. Store that in i.
k=Position

Store the Position function in k. (to reduce byte-count when using Position again)
Flatten@Outer[...,{i[[#]]},j,1]

Find the inverse permutation of the N-th permutation.
Max@k[i,...]

Find the k (Position) of the inverse permutation in i (all permutations)
Using built-ins, 46 43 bytes
a[(a=Ordering)/@Permutations@Range@#][[#]]&amp;

1-indexed.