In physics and mathematics, the Pauli group G_1 on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix I and all of the Pauli matrices together with the products of these matrices with the factors \pm 1 and \pm i: The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on n qubits, G_n, is the group generated by the operators described above applied to each of n qubits in the tensor product Hilbert space. That is, The order of G_n is 4 \cdot 4^n since a scalar \pm 1 or \pm i factor in any tensor position can be moved to any other position. As an abstract group, is the central product of a cyclic group of order 4 and the dihedral group of order 8. The Pauli group is a representation of the gamma group in three-dimensional Euclidean space. It is not isomorphic to the gamma group; it is less free, in that its chiral element is whereas there is no such relationship for the gamma group.