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 + 1/2 | (3) -y, x, z + 1/4 | (4) y, -x, z + 3/4 |
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I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b
| C41 (76, P41) | <2; 3> | a - b, a + b, c | |
| C41 (76, P41) | <2 + (1, 1, 0); 3 + (1, 0, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
[3] c' = 3c
| P43 (78) | <2 + (0, 0, 1); 3 + (0, 0, 2)> | a, b, 3c | |
- Series of maximal isomorphic subgroups
[p] c' = pc
| P43 (78) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, 3p/4 - 1/4)> | a, b, pc | | | | p > 2; p ≡ 3 (mod 4)
no conjugate subgroups |
| P41 (76) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/4 - 1/4)> | a, b, pc | | | | p > 4; p ≡ 1 (mod 4)
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| P41 (76) | <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
| P41 (76) | <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] P4122 (91); [2] P41212 (92) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
