Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
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 | | (5) x + 1/2, -y + 1/2, z + 1/2 | (6) -x + 1/2, y + 1/2, z + 1/2 | (7) y + 1/2, x + 1/2, -z + 1/2 | (8) -y + 1/2, -x + 1/2, -z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] P-411 (81, P-4) | 1; 2; 3; 4 |
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| [2] P2n1 (34, Pnn2) | 1; 2; 5; 6 |
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| [2] P212 (21, C222) | 1; 2; 7; 8 | a - b, a + b, c
| 0, 1/2, 1/4
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| F-4d2 (122, I-42d) | <2; 3; 5> | a - b, a + b, 2c | |
| F-4d2 (122, I-42d) | <2; 5; 3 + (0, 0, 1)> | a - b, a + b, 2c | 0, 0, 1/2 |
| F-4d2 (122, I-42d) | <2; 3 + (1, 0, 0); 5 + (0, 1, 0)> | a - b, a + b, 2c | 1/2, 1/2, 0 |
| F-4d2 (122, I-42d) | <2; 3 + (1, 0, 1); 5 + (0, 1, 0)> | a - b, a + b, 2c | 1/2, 1/2, 1/2 |
[3] c' = 3c
 | P-4n2 (118) | <2; 3; 5 + (0, 0, 1)> | a, b, 3c | | | P-4n2 (118) | <2; 3 + (0, 0, 2); 5 + (0, 0, 1)> | a, b, 3c | 0, 0, 1 | | P-4n2 (118) | <2; 3 + (0, 0, 4); 5 + (0, 0, 1)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P-4n2 (118) | <2; 3 + (0, 0, 2u); 5 + (0, 0, p/2 - 1/2)> | 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-4n2 (118) | <2 + (2u, 2v, 0); 3 + (u - v, u + v, 0); 5 + (p/2 - 1/2, p/2 - 1/2 + 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P4/nnc (126); [2] P4/mnc (128); [2] P42/nnm (134); [2] P42/mnm (136) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C-4c2 (112, P-42c); [2] I-4m2 (119) |
| [2] c' = 1/2c P-4b2 (117) |
