Topologically ordered phases can host interesting classes of non-trivial topological defects of varying codimensions. Among the topological defects, the invertible defects form an algebraic structure called higher-group. In this talk we explain how the higher-group structure of invertible global symmetry emerges in discrete gauge theory of generic dimensions, and show various examples of the higher-group symmetry in topological order mainly focusing on (3+1)-dimensional stabilizer codes. The emergent global symmetry of a stabilizer model is understood as a logical gate acting on the logical qubits. We explain that the higher-group structure of global symmetry in general leads to non-Pauli logical gate realized by the action of emergent global symmetry, e.g., Control-Z logical gate of (3+1)-dimensional Z2 toric code.