Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) y, -x, -z | (4) -y, x, -z |
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I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] c' = 2c
| P-4 (81) | <2; 3> | a, b, 2c | |
| P-4 (81) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] a' = 2a, b' = 2b
| C-4 (81, P-4) | <2; 3> | a - b, a + b, c | |
| C-4 (81, P-4) | <2 + (1, 1, 0); 3 + (0, 1, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
[2] a' = 2a, b' = 2b, c' = 2c
| F-4 (82, I-4) | <2; 3> | a - b, a + b, 2c | |
| F-4 (82, I-4) | <2; 3 + (0, 0, 1)> | a - b, a + b, 2c | 0, 0, 1/2 |
[3] c' = 3c
 | P-4 (81) | <2; 3> | a, b, 3c | | | P-4 (81) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P-4 (81) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P-4 (81) | <2; 3 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p2] a' = pa, b' = pb
| P-4 (81) | <2 + (2u, 2v, 0); 3 + (u - v, u + v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 3 (mod 4) |
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[p = q2 + r2] a' = qa - rb, b' = ra + qb
| P-4 (81) | <2 + (2u, 0, 0); 3 + (u, u, 0)> | qa - rb, ra + qb, c | u, 0, 0 | | | q > 0; r > 0; p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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I Minimal translationengleiche supergroups
| [2] P4/m (83); [2] P42/m (84); [2] P4/n (85); [2] P42/n (86); [2] P-42m (111); [2] P-42c (112); [2] P-421m (113); [2] P-421c (114); [2] P-4m2 (115); [2] P-4c2 (116); [2] P-4b2 (117); [2] P-4n2 (118) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
