P41 No. 76 C42

 P41 P43 Axes Coordinates Wyckoff positions Axes Coordinates 4a I Maximal translationengleiche subgroups [2] P1121 (4) 2 × 2a [2] P1121 (4) II Maximal klassengleiche subgroups Enlarged unit cell, isomorphic [3] P43 (78) a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 4a [3] P41 (76) a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) [p] P43 (78) a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 4a [p] P41 (76) a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p = prime = 4n - 1; u = 1, . . ., p - 1 p = prime = 4n - 1; u = 1, . . ., p - 1 [5] P41 a, b, 5c x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) 5 × 4a [5] P43 a, b, 5c x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) [p] P41 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 4a [p] P43 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p = prime = 4n + 1; u = 1, . . ., p - 1 p = prime = 4n + 1; u = 1, . . ., p - 1 [2] P41 a - b, (1/2)(x - y), (1/2)(x + y), z; +((1/2), (1/2), 0) 2 × 4a [2] P43 a - b, (1/2)(x - y), (1/2)(x + y), z; +((1/2), (1/2), 0) a + b, c a + b, c [2] P41 a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), z; +((1/2), (1/2), 0) 2 × 4a [2] P43 a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), z; +((1/2), (1/2), 0) a + b, c a + b, c [5] P41 a + 2b, (1/5)(x + 2y), (1/5)(-2x + y), z; 5 × 4a [5] P43 a + 2b, (1/5)(x + 2y), (1/5)(-2x + y), z; -2a + b, c ±((1/5), (3/5), 0); ±((2/5), (1/5), 0) -2a + b, c ±((1/5), (3/5), 0); ±((2/5), (1/5), 0) [5] P41 a - 2b, (1/5)(x - 2y), (1/5)(2x + y), z; 5 × 4a [5] P43 a - 2b, (1/5)(x - 2y), (1/5)(2x + y), z; 2a + b, c ±((1/5), (2/5), 0); ±((3/5), (1/5), 0) 2a + b, c ±((1/5), (2/5), 0); ±((3/5), (1/5), 0) [p] P41 qa - rb, (1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) p × 4a [p] P43 qa - rb, (1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) ra + qb, c q = 2n + 1 ≥ 1; r = ± 2n'≠ 0 ra + qb, c q = 2n + 1 ≥ 1; r = ± 2n'≠ 0 p = q2 + r2 = prime = 4n + 1; u = 1, . . ., p - 1 p = q2 + r2 = prime = 4n + 1; u = 1, . . ., p - 1 [9] P41 3a, 3b, c (1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); 9 × 4a [9] P43 3a, 3b, c (1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); ±((1/3), (1/3), 0); ±((1/3), (2/3), 0) ±((1/3), (1/3), 0); ±((1/3), (2/3), 0) [p2] P41 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) p2 × 4a [p2] P43 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) p = prime = 4n - 1; u, v = 1, . . ., p - 1 p = prime = 4n - 1; u, v = 1, . . ., p - 1