Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) -y, x, z + 1/2 | (4) y, -x, z + 1/2 | | (5) -x, y, -z + 1/2 | (6) x, -y, -z + 1/2 | (7) y, x, -z | (8) -y, -x, -z | | (9) -x, -y, -z | (10) x, y, -z | (11) y, -x, -z + 1/2 | (12) -y, x, -z + 1/2 | | (13) x, -y, z + 1/2 | (14) -x, y, z + 1/2 | (15) -y, -x, z | (16) y, x, z |
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I Maximal translationengleiche subgroups
| [2] P-4c2 (116) | 1; 2; 7; 8; 11; 12; 13; 14 |
| 0, 0, 1/4
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| [2] P-42m (111) | 1; 2; 5; 6; 11; 12; 15; 16 |
| 0, 0, 1/4
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| [2] P42cm (101) | 1; 2; 3; 4; 13; 14; 15; 16 |
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| [2] P4222 (93) | 1; 2; 3; 4; 5; 6; 7; 8 |
| 0, 0, 1/4
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| [2] P42/m11 (84, P42/m) | 1; 2; 3; 4; 9; 10; 11; 12 |
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| [2] P2/m12/m (65, Cmmm) | 1; 2; 7; 8; 9; 10; 15; 16 | a - b, a + b, c
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| [2] P2/m2/c1 (49, Pccm) | 1; 2; 5; 6; 9; 10; 13; 14 |
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b
| C42/ecm (137, P42/nmc) | <2; 3; (5; 9) + (1, 0, 0)> | a - b, a + b, c | 1/2, 0, 0 |
| C42/ecm (137, P42/nmc) | <2; 5; (3; 9) + (1, 0, 0)> | a - b, a + b, c | 0, 1/2, 0 |
| C42/mcd (135, P42/mbc) | <2; 3; 9; 5 + (1, 0, 0)> | a - b, a + b, c | |
| C42/mcd (135, P42/mbc) | <2; 5; 9; 3 + (1, 0, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
| C42/ecd (133, P42/nbc) | <2; 3; 5; 9 + (1, 0, 0)> | a - b, a + b, c | 1/2, 0, 0 |
| C42/ecd (133, P42/nbc) | <2; (3; 5; 9) + (1, 0, 0)> | a - b, a + b, c | 0, 1/2, 0 |
| C42/mcm (131, P42/mmc) | <2; 3; 5; 9> | a - b, a + b, c | |
| C42/mcm (131, P42/mmc) | <2; 9; (3; 5) + (1, 0, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
[3] c' = 3c
 | P42/mcm (132) | <2; 9; (3; 5) + (0, 0, 1)> | a, b, 3c | | | P42/mcm (132) | <2; 3 + (0, 0, 1); 5 + (0, 0, 3); 9 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P42/mcm (132) | <2; 3 + (0, 0, 1); 5 + (0, 0, 5); 9 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P42/mcm (132) | <2; 3 + (0, 0, p/2 - 1/2); 5 + (0, 0, p/2 - 1/2 + 2u); 9 + (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
| P42/mcm (132) | <(2; 9) + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (2u, 0, 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
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C42/mcm (131, P42/mmc); [2] I4/mcm (140) |
| [2] c' = 1/2c P4/mmm (123) |
