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 |
|
| | (0, 0, 0)+ (0, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x, -y, z | (3) x + 1/2, -y + 1/2, z | (4) -x + 1/2, y + 1/2, z |
|
I Maximal translationengleiche subgroups
| [2] A1a1 (9, C1c1) | (1; 3)+ | c, b, -a
| 0, 1/4, 0
|
| [2] Ae11 (7, P1c1) | (1; 4)+ | 1/2(-b + c), a, b
| 1/4, 0, 0
|
| [2] A112 (5) | (1; 2)+ |
|
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pbn21 (33, Pna21) | 1; 4; (2; 3) + (0, 1/2, 1/2) | -b, a, c | 0, 1/4, 0 |
| [2] Pba2 (32) | 1; 2; 3; 4 | | |
| [2] Pcn2 (30, Pnc2) | 1; 2; (3; 4) + (0, 1/2, 1/2) | -b, a, c | |
| [2] Pca21 (29) | 1; 3; (2; 4) + (0, 1/2, 1/2) | | 0, 1/4, 0 |
[3] a' = 3a
 | Aea2 (41) | <2; 3 + (1, 0, 0)> | 3a, b, c | | | Aea2 (41) | <2 + (2, 0, 0); 3 + (1, 0, 0)> | 3a, b, c | 1, 0, 0 | | Aea2 (41) | <2 + (4, 0, 0); 3 + (1, 0, 0)> | 3a, b, c | 2, 0, 0 |
|
[3] b' = 3b
| Aea2 (41) | <2; 3 + (0, 1, 0)> | a, 3b, c | | | Aea2 (41) | <2 + (0, 2, 0); 3 + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Aea2 (41) | <2 + (0, 4, 0); 3 + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
|
[3] c' = 3c
- Series of maximal isomorphic subgroups
[p] a' = pa
| Aea2 (41) | <2 + (2u, 0, 0); 3 + (p/2 - 1/2, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] b' = pb
| Aea2 (41) | <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 |
|
[p] c' = pc
| Aea2 (41) | <2; 3> | a, b, pc | | | | p > 2
no conjugate subgroups |
|
I Minimal translationengleiche supergroups
| [2] Cmce (64); [2] Ccce (68) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] b' = 1/2b, c' = 1/2c Pma2 (28); [2] a' = 1/2a Aem2 (39) |
