  Higher symmetries can emerge at low energies in a topologically ordered state
with no symmetry, when some topological excitations have very high energy
scales while other topological excitations have low energies. The low energy
properties of topological orders in this limit, with the emergent higher
symmetries, may be described by higher symmetry protected topological order.
This motivates us, as a simplest example, to study a lattice model of
$\mathbb{Z}_n$-1-symmetry protected topological (1-SPT) states in 3+1D for even
$n$. We write down an exactly solvable lattice model and study its boundary
transformation. On the boundary, we show the existence of anyons with
non-trivial self-statistics. For the $n=2$ case, where the bulk classification
is given by an integer $m$ mod $4$, we show that the boundary can be gapped
with double semion topological order for $m=1$ and toric code for $m=2$. The
bulk ground state wavefunction amplitude is given in terms of the linking
numbers of loops in the dual lattice. Our construction can be generalized to
arbitrary 1-SPT protected by finite unitary symmetry.
