I4 No. 79 C45

 Axes Coordinates Wyckoff positions 2a 4b 8c I Maximal translationengleiche subgroups [2] I112 (5) 2a 2 × 2b 2 × 4c A112 a, -a + b, c x + y, y, z II Maximal klassengleiche subgroups Loss of centring translations [2] P42 (77) x + (1/2), y, z 2c 2a; 2b 2 × 4d [2] P4 (75) 1a; 1b 2 × 2c 2 × 4d Enlarged unit cell, isomorphic [3] I4 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 2a 3 × 4b 3 × 8c [p] I4 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 2a p × 4b p × 8c p = prime > 2; u = 1, . . ., p - 1 [5] I4 a + 2b, -2a + b, c (1/5)(x + 2y), (1/5)(-2x + y), z; ±((2/5), (1/5), 0); ±((1/5), (3/5), 0) 2a; 8c 4b; 2 × 8c 5 × 8c [5] I4 a - 2b, 2a + b, c (1/5)(x - 2y), (1/5)(2x + y), z; ±((3/5), (1/5), 0); ±((1/5), (2/5), 0) 2a; 8c 4b; 2 × 8c 5 × 8c [p] I4 qa - rb, (1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) 2a; ((p - 1)/4) × 8c 4b; ((p - 1)/2) × 8c p × 4d ra + qb, c q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; p = q2 + r2 = prime = 4n + 1; u = 1, . . ., p - 1 [9] I4 3a, 3b, c (1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); 2a; 2 × 8c 4b; 4 × 8c 9 × 8c ±((1/3), (1/3), 0); ±((1/3), (2/3), 0) [p2] I4 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 2a; ((p2 - 1)/4) × 8c 4b; ((p2 - 1)/2) × 8c p2 × 4d p = prime = 4n - 1; u, v = 1, . . ., p - 1