Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (0, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x, -y, z | (3) x, -y + 1/2, z | (4) -x, y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] A1m1 (8, C1m1) | (1; 3)+ | c, b, -a - c
| 0, 1/4, 0
|
| [2] Ae11 (7, P1c1) | (1; 4)+ | 1/2(-b + c), a, b
|
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| [2] A112 (5) | (1; 2)+ |
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pbc21 (29, Pca21) | 1; 4; (2; 3) + (0, 1/2, 1/2) | -b, a, c | 0, 1/4, 0 |
| [2] Pbm2 (28, Pma2) | 1; 2; 3; 4 | -b, a, c | |
| [2] Pcc2 (27) | 1; 2; (3; 4) + (0, 1/2, 1/2) | | |
| [2] Pcm21 (26, Pmc21) | 1; 3; (2; 4) + (0, 1/2, 1/2) | -b, a, c | 0, 1/4, 0 |
[2] a' = 2a
| Ibm2 (46, Ima2) | <2; 3> | -b, 2a, c | |
| Ibm2 (46, Ima2) | <3; 2 + (1, 0, 0)> | -b, 2a, c | 1/2, 0, 0 |
| Iba2 (45) | <2; 3 + (1, 0, 0)> | 2a, b, c | |
| Iba2 (45) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| Aea2 (41) | <2; 3 + (1, 0, 0)> | 2a, b, c | |
| Aea2 (41) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| Aem2 (39) | <2; 3> | 2a, b, c | |
| Aem2 (39) | <3; 2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[3] a' = 3a
 | Aem2 (39) | <2; 3> | 3a, b, c | | | Aem2 (39) | <3; 2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Aem2 (39) | <3; 2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Aem2 (39) | <2; 3 + (0, 1, 0)> | a, 3b, c | | | Aem2 (39) | <2 + (0, 2, 0); 3 + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Aem2 (39) | <2 + (0, 4, 0); 3 + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
- Series of maximal isomorphic subgroups
[p] a' = pa
| Aem2 (39) | <3; 2 + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] b' = pb
| Aem2 (39) | <2 + (0, 2u, 0); 3 + (0, p/2 - 1/2 + 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| Aem2 (39) | <2; 3> | a, b, pc | | | | p > 2
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] Cmce (64); [2] Cmme (67) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] b' = 1/2b, c' = 1/2c Pmm2 (25) |
