UNIQUE AXIS b
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x, y, -z | (3) -x, -y, -z | (4) x, -y, z |
|
I Maximal translationengleiche subgroups
| [2] P1m1 (6) | 1; 4 |
|
|
| [2] P121 (3) | 1; 2 |
|
|
| [2] P-1 (2) | 1; 3 |
|
|
II Maximal klassengleiche subgroups
[2] b' = 2b
| P121/m1 (11) | <3; 2 + (0, 1, 0)> | a, 2b, c | |
| P121/m1 (11) | <(2; 3) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
| P12/m1 (10) | <2; 3> | a, 2b, c | |
| P12/m1 (10) | <2; 3 + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] c' = 2c
| P12/c1 (13) | <3; 2 + (0, 0, 1)> | a, b, 2c | |
| P12/c1 (13) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P12/m1 (10) | <2; 3> | a, b, 2c | |
| P12/m1 (10) | <(2; 3) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] a' = 2a
| P12/a1 (13, P12/c1) | <3; 2 + (1, 0, 0)> | -2a - c, b, 2a | |
| P12/a1 (13, P12/c1) | <2; 3 + (1, 0, 0)> | -2a - c, b, 2a | 1/2, 0, 0 |
| P12/m1 (10) | <2; 3> | 2a, b, c | |
| P12/m1 (10) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] a' = 2a, c' = 2c
| B12/e1 (13, P12/c1) | <3; 2 + (0, 0, 1)> | a - c, b, 2c | |
| B12/e1 (13, P12/c1) | <2; 3 + (0, 0, 1)> | a - c, b, 2c | 0, 0, 1/2 |
| B12/m1 (10, P12/m1) | <2; 3> | a - c, b, 2c | |
| B12/m1 (10, P12/m1) | <(2; 3) + (0, 0, 1)> | a - c, b, 2c | 0, 0, 1/2 |
[2] a' = 2a, b' = 2b
| C12/m1 (12) | <2; 3> | 2a, 2b, c | |
| C12/m1 (12) | <2; 3 + (0, 1, 0)> | 2a, 2b, c | 0, 1/2, 0 |
| C12/m1 (12) | <(2; 3) + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| C12/m1 (12) | <2 + (1, 0, 0); 3 + (1, 1, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
[2] b' = 2b, c' = 2c
| A12/m1 (12, C12/m1) | <2; 3> | 2c, 2b, -a - 2c | |
| A12/m1 (12, C12/m1) | <(2; 3) + (0, 0, 1)> | 2c, 2b, -a - 2c | 0, 0, 1/2 |
| A12/m1 (12, C12/m1) | <2; 3 + (0, 1, 0)> | 2c, 2b, -a - 2c | 0, 1/2, 0 |
| A12/m1 (12, C12/m1) | <2 + (0, 0, 1); 3 + (0, 1, 1)> | 2c, 2b, -a - 2c | 0, 1/2, 1/2 |
[2] a' = 2a, b' = 2b, c' = 2c
| F12/m1 (12, C12/m1) | <2; 3> | 2a, 2b, -a + c | |
| F12/m1 (12, C12/m1) | <2; 3 + (0, 1, 0)> | 2a, 2b, -a + c | 0, 1/2, 0 |
| F12/m1 (12, C12/m1) | <(2; 3) + (1, 0, 0)> | 2a, 2b, -a + c | 1/2, 0, 0 |
| F12/m1 (12, C12/m1) | <2 + (1, 0, 0); 3 + (1, 1, 0)> | 2a, 2b, -a + c | 1/2, 1/2, 0 |
[3] b' = 3b
 | P12/m1 (10) | <2; 3> | a, 3b, c | | | P12/m1 (10) | <2; 3 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P12/m1 (10) | <2; 3 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
|
[3] c' = 3c
| P12/m1 (10) | <2; 3> | a, b, 3c | | | P12/m1 (10) | <(2; 3) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P12/m1 (10) | <(2; 3) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
|
[3] a' = a - c, c' = 3c
| P12/m1 (10) | <2; 3> | a - c, b, 3c | | | P12/m1 (10) | <(2; 3) + (0, 0, 2)> | a - c, b, 3c | 0, 0, 1 | | P12/m1 (10) | <(2; 3) + (0, 0, 4)> | a - c, b, 3c | 0, 0, 2 |
|
[3] a' = a - 2c, c' = 3c
| P12/m1 (10) | <2; 3> | a - 2c, b, 3c | | | P12/m1 (10) | <(2; 3) + (0, 0, 2)> | a - 2c, b, 3c | 0, 0, 1 | | P12/m1 (10) | <(2; 3) + (0, 0, 4)> | a - 2c, b, 3c | 0, 0, 2 |
|
[3] a' = 3a
| P12/m1 (10) | <2; 3> | 3a, b, c | | | P12/m1 (10) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P12/m1 (10) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
|
- Series of maximal isomorphic subgroups
[p] b' = pb
| P12/m1 (10) | <2; 3 + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] a' = a - qc, c' = pc
| P12/m1 (10) | <(2; 3) + (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 |
|
[p] a' = pa
| P12/m1 (10) | <(2; 3) + (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] Pmmm (47); [2] Pccm (49); [2] Pmma (51); [2] Pmna (53); [2] Pbam (55); [2] Pnnm (58); [2] Cmmm (65); [2] Cccm (66); [2] P4/m (83); [2] P42/m (84); [3] P6/m (175) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C12/m1 (12); [2] A12/m1 (12, C12/m1); [2] I12/m1 (12, C12/m1) |
UNIQUE AXIS c
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x, -y, z | (3) -x, -y, -z | (4) x, y, -z |
|
I Maximal translationengleiche subgroups
| [2] P11m (6) | 1; 4 |
|
|
| [2] P112 (3) | 1; 2 |
|
|
| [2] P-1 (2) | 1; 3 |
|
|
II Maximal klassengleiche subgroups
[2] c' = 2c
| P1121/m (11) | <3; 2 + (0, 0, 1)> | a, b, 2c | |
| P1121/m (11) | <(2; 3) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P112/m (10) | <2; 3> | a, b, 2c | |
| P112/m (10) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] a' = 2a
| P112/a (13) | <3; 2 + (1, 0, 0)> | 2a, b, c | |
| P112/a (13) | <2; 3 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| P112/m (10) | <2; 3> | 2a, b, c | |
| P112/m (10) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| P112/b (13, P112/a) | <3; 2 + (0, 1, 0)> | 2b, -a - 2b, c | |
| P112/b (13, P112/a) | <2; 3 + (0, 1, 0)> | 2b, -a - 2b, c | 0, 1/2, 0 |
| P112/m (10) | <2; 3> | a, 2b, c | |
| P112/m (10) | <(2; 3) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] a' = 2a, b' = 2b
| C112/e (13, P112/a) | <3; 2 + (1, 0, 0)> | 2a, -a + b, c | |
| C112/e (13, P112/a) | <2; 3 + (1, 0, 0)> | 2a, -a + b, c | 1/2, 0, 0 |
| C112/m (10, P112/m) | <2; 3> | 2a, -a + b, c | |
| C112/m (10, P112/m) | <(2; 3) + (1, 0, 0)> | 2a, -a + b, c | 1/2, 0, 0 |
[2] b' = 2b, c' = 2c
| A112/m (12) | <2; 3> | a, 2b, 2c | |
| A112/m (12) | <2; 3 + (0, 0, 1)> | a, 2b, 2c | 0, 0, 1/2 |
| A112/m (12) | <(2; 3) + (0, 1, 0)> | a, 2b, 2c | 0, 1/2, 0 |
| A112/m (12) | <2 + (0, 1, 0); 3 + (0, 1, 1)> | a, 2b, 2c | 0, 1/2, 1/2 |
[2] a' = 2a, c' = 2c
| B112/m (12, A112/m) | <2; 3> | -2a - b, 2a, 2c | |
| B112/m (12, A112/m) | <(2; 3) + (1, 0, 0)> | -2a - b, 2a, 2c | 1/2, 0, 0 |
| B112/m (12, A112/m) | <2; 3 + (0, 0, 1)> | -2a - b, 2a, 2c | 0, 0, 1/2 |
| B112/m (12, A112/m) | <2 + (1, 0, 0); 3 + (1, 0, 1)> | -2a - b, 2a, 2c | 1/2, 0, 1/2 |
[2] a' = 2a, b' = 2b, c' = 2c
| F112/m (12, A112/m) | <2; 3> | a - b, 2b, 2c | |
| F112/m (12, A112/m) | <2; 3 + (0, 0, 1)> | a - b, 2b, 2c | 0, 0, 1/2 |
| F112/m (12, A112/m) | <(2; 3) + (0, 1, 0)> | a - b, 2b, 2c | 0, 1/2, 0 |
| F112/m (12, A112/m) | <2 + (0, 1, 0); 3 + (0, 1, 1)> | a - b, 2b, 2c | 0, 1/2, 1/2 |
[3] c' = 3c
| P112/m (10) | <2; 3> | a, b, 3c | | | P112/m (10) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P112/m (10) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
|
[3] a' = 3a
| P112/m (10) | <2; 3> | 3a, b, c | | | P112/m (10) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P112/m (10) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
|
[3] a' = 3a, b' = -a + b
| P112/m (10) | <2; 3> | 3a, -a + b, c | | | P112/m (10) | <(2; 3) + (2, 0, 0)> | 3a, -a + b, c | 1, 0, 0 | | P112/m (10) | <(2; 3) + (4, 0, 0)> | 3a, -a + b, c | 2, 0, 0 |
|
[3] a' = 3a, b' = -2a + b
| P112/m (10) | <2; 3> | 3a, -2a + b, c | | | P112/m (10) | <(2; 3) + (2, 0, 0)> | 3a, -2a + b, c | 1, 0, 0 | | P112/m (10) | <(2; 3) + (4, 0, 0)> | 3a, -2a + b, c | 2, 0, 0 |
|
[3] b' = 3b
| P112/m (10) | <2; 3> | a, 3b, c | | | P112/m (10) | <(2; 3) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P112/m (10) | <(2; 3) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
|
- Series of maximal isomorphic subgroups
[p] c' = pc
| P112/m (10) | <2; 3 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] a' = pa, b' = -qa + b
| P112/m (10) | <(2; 3) + (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
| P112/m (10) | <(2; 3) + (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] Pmmm (47); [2] Pccm (49); [2] Pmma (51); [2] Pmna (53); [2] Pbam (55); [2] Pnnm (58); [2] Cmmm (65); [2] Cccm (66); [2] P4/m (83); [2] P42/m (84); [3] P6/m (175) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A112/m (12); [2] B112/m (12, A112/m); [2] I112/m (12, A112/m) |
