  We demonstrate that multipartite entanglement is able to characterize
one-dimensional symmetry-protected topological order, which is witnessed by the
scaling behavior of the quantum Fisher information of the ground state with
respect to the spin operators defined in the dual lattice. We investigate an
extended Kitaev chain with a $\mathbf{Z}$ symmetry identified equivalently by
winding numbers and paired Majorana zero modes at each end. The topological
phases with high winding numbers are detected by the scaling coefficient of the
quantum Fisher information density with respect to generators in different dual
lattices. Containing richer properties and more complex structures than
bipartite entanglement, the dual multipartite entanglement of the topological
state has promising applications in robust quantum computation and quantum
metrology, and can be generalized to identify topological order in the Kitaev
honeycomb model.
