Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z |
|
I Maximal translationengleiche subgroups
| [2] I112 (5, A112) | (1; 2)+ | b, -a - b, c
|
|
| [2] I121 (5, C121) | (1; 3)+ | -a - c, b, a
|
|
| [2] I211 (5, C121) | (1; 4)+ | -b - c, a, c
|
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P21212 (18) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | | 0, 0, 1/4 |
| [2] P21221 (18, P21212) | 1; 3; (2; 4) + (1/2, 1/2, 1/2) | c, a, b | 0, 1/4, 0 |
| [2] P22121 (18, P21212) | 1; 4; (2; 3) + (1/2, 1/2, 1/2) | b, c, a | 1/4, 0, 0 |
| [2] P222 (16) | 1; 2; 3; 4 | | |
[3] a' = 3a
 | I222 (23) | <2; 3> | 3a, b, c | | | I222 (23) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | I222 (23) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
|
[3] b' = 3b
| I222 (23) | <2; 3> | a, 3b, c | | | I222 (23) | <3; 2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | I222 (23) | <3; 2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
|
[3] c' = 3c
| I222 (23) | <2; 3> | a, b, 3c | | | I222 (23) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | I222 (23) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
|
- Series of maximal isomorphic subgroups
[p] a' = pa
| I222 (23) | <(2; 3) + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] b' = pb
| I222 (23) | <3; 2 + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] c' = pc
| I222 (23) | <2; 3 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
I Minimal translationengleiche supergroups
| [2] Immm (71); [2] Ibam (72); [2] I422 (97); [2] I-42m (121); [3] I23 (197) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a A222 (21, C222); [2] b' = 1/2b B222 (21, C222); [2] c' = 1/2c C222 (21) |
