UNIQUE AXIS b
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x, y + 1/2, -z | |
|
I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] c' = 2c
| P1211 (4) | <2> | a, b, 2c | |
| P1211 (4) | <2 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] a' = 2a
| P1211 (4) | <2> | 2a, b, c | |
| P1211 (4) | <2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] a' = 2a, c' = 2c
| B1211 (4, P1211) | <2> | a - c, b, 2c | |
| B1211 (4, P1211) | <2 + (0, 0, 1)> | a - c, b, 2c | 0, 0, 1/2 |
[3] b' = 3b
| P1211 (4) | <2 + (0, 1, 0)> | a, 3b, c | |
[3] c' = 3c
 | P1211 (4) | <2> | a, b, 3c | | | P1211 (4) | <2 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P1211 (4) | <2 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = a - c, c' = 3c
| P1211 (4) | <2> | a - c, b, 3c | | | P1211 (4) | <2 + (0, 0, 2)> | a - c, b, 3c | 0, 0, 1 | | P1211 (4) | <2 + (0, 0, 4)> | a - c, b, 3c | 0, 0, 2 |
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[3] a' = a - 2c, c' = 3c
| P1211 (4) | <2> | a - 2c, b, 3c | | | P1211 (4) | <2 + (0, 0, 2)> | a - 2c, b, 3c | 0, 0, 1 | | P1211 (4) | <2 + (0, 0, 4)> | a - 2c, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| P1211 (4) | <2> | 3a, b, c | | | P1211 (4) | <2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P1211 (4) | <2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| P1211 (4) | <2 + (0, p/2 - 1/2, 0)> | a, pb, c | | | | p > 2
no conjugate subgroups |
|
[p] a' = a - qc, c' = pc
| P1211 (4) | <2 + (0, 0, 2u)> | a - qc, b, pc | 0, 0, u | | | p > 2; 0 ≤ q < p; 0 ≤ u < p
p conjugate subgroups for each pair of q and prime p |
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[p] a' = pa
| P1211 (4) | <2 + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
I Minimal translationengleiche supergroups
| [2] P121/m1 (11); [2] P121/c1 (14); [2] P2221 (17); [2] P21212 (18); [2] P212121 (19); [2] C2221 (20); [2] Pmc21 (26); [2] Pca21 (29); [2] Pmn21 (31); [2] Pna21 (33); [2] Cmc21 (36); [2] P41 (76); [2] P43 (78); [3] P61 (169); [3] P65 (170); [3] P63 (173) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C121 (5); [2] A121 (5, C121); [2] I121 (5, C121) |
UNIQUE AXIS c
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x, -y, z + 1/2 | |
|
I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] a' = 2a
| P1121 (4) | <2> | 2a, b, c | |
| P1121 (4) | <2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| P1121 (4) | <2> | a, 2b, c | |
| P1121 (4) | <2 + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] a' = 2a, b' = 2b
| C1121 (4, P1121) | <2> | 2a, -a + b, c | |
| C1121 (4, P1121) | <2 + (1, 0, 0)> | 2a, -a + b, c | 1/2, 0, 0 |
[3] c' = 3c
| P1121 (4) | <2 + (0, 0, 1)> | a, b, 3c | |
[3] a' = 3a
| P1121 (4) | <2> | 3a, b, c | | | P1121 (4) | <2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P1121 (4) | <2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -a + b
| P1121 (4) | <2> | 3a, -a + b, c | | | P1121 (4) | <2 + (2, 0, 0)> | 3a, -a + b, c | 1, 0, 0 | | P1121 (4) | <2 + (4, 0, 0)> | 3a, -a + b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -2a + b
| P1121 (4) | <2> | 3a, -2a + b, c | | | P1121 (4) | <2 + (2, 0, 0)> | 3a, -2a + b, c | 1, 0, 0 | | P1121 (4) | <2 + (4, 0, 0)> | 3a, -2a + b, c | 2, 0, 0 |
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[3] b' = 3b
| P1121 (4) | <2> | a, 3b, c | | | P1121 (4) | <2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P1121 (4) | <2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P1121 (4) | <2 + (0, 0, p/2 - 1/2)> | a, b, pc | | | | p > 2
no conjugate subgroups |
|
[p] a' = pa, b' = -qa + b
| P1121 (4) | <2 + (2u, 0, 0)> | pa, -qa + b, c | u, 0, 0 | | | p > 2; 0 ≤ q < p; 0 ≤ u < p
p conjugate subgroups for each pair of q and prime p |
|
[p] b' = pb
| P1121 (4) | <2 + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
I Minimal translationengleiche supergroups
| [2] P1121/m (11); [2] P1121/a (14); [2] P2221 (17); [2] P21212 (18); [2] P212121 (19); [2] C2221 (20); [2] Pmc21 (26); [2] Pca21 (29); [2] Pmn21 (31); [2] Pna21 (33); [2] Cmc21 (36); [2] P41 (76); [2] P43 (78); [3] P61 (169); [3] P65 (170); [3] P63 (173) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A112 (5); [2] B112 (5, A112); [2] I112 (5, A112) |
