Table 2 List of XBdG for class DIII systems with P1̄ (20), P4, and P4/m symmetry in each spatial dimension.

SG (rep of Δk)1D2D3D
P1̄ (Au)2(ℤ2)2 × ℤ4(ℤ2)3 × (ℤ4)3 × ℤ8
P4 (B)122
P4/m (Au)(ℤ2)22 × ℤ8(ℤ2)4 × ℤ4 × ℤ8 × ℤ16
P4/m (Bu)12 × ℤ82 × (ℤ4)2 × ℤ8
P4/m (Bg)1(ℤ2)2(ℤ2)3