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 + 1/2, x + 1/2, z + 1/2 | (4) y + 1/2, -x + 1/2, z + 1/2 | | (5) -x + 1/2, y + 1/2, -z + 1/2 | (6) x + 1/2, -y + 1/2, -z + 1/2 | (7) y, x, -z | (8) -y, -x, -z |
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I Maximal translationengleiche subgroups
| [2] P4211 (77, P42) | 1; 2; 3; 4 |
| 0, 1/2, 0
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| [2] P212 (21, C222) | 1; 2; 7; 8 | a - b, a + b, c
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| [2] P2211 (18, P21212) | 1; 2; 5; 6 |
| 0, 0, 1/4
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P43212 (96) | <5; (2; 3) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P43212 (96) | <(2; 3; 5) + (0, 0, 1)> | a, b, 2c | |
| P41212 (92) | <3; 5; 2 + (0, 0, 1)> | a, b, 2c | |
| P41212 (92) | <3; (2; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] c' = 3c
 | P42212 (94) | <2; (3; 5) + (0, 0, 1)> | a, b, 3c | | | P42212 (94) | <2; 3 + (0, 0, 1); 5 + (0, 0, 3)> | a, b, 3c | 0, 0, 1 | | P42212 (94) | <2; 3 + (0, 0, 1); 5 + (0, 0, 5)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P42212 (94) | <2; 3 + (0, 0, p/2 - 1/2); 5 + (0, 0, p/2 - 1/2 + 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
| P42212 (94) | <2 + (2u, 2v, 0); 3 + (p/2 - 1/2 + u + v, p/2 - 1/2 - u + v, 0); 5 + (p/2 - 1/2 + 2u, p/2 - 1/2, 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] P42/mbc (135); [2] P42/mnm (136); [2] P42/nmc (137); [2] P42/ncm (138) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C4222 (93, P4222); [2] I422 (97) |
