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 |
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| | (1) x, y, z | (2) -x, y + 1/2, -z | (3) -x, -y, -z | (4) x, -y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] P1m1 (6) | 1; 4 |
| 0, 1/4, 0
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| [2] P1211 (4) | 1; 2 |
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| [2] P-1 (2) | 1; 3 |
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P121/c1 (14) | <3; 2 + (0, 0, 1)> | a, b, 2c | |
| P121/c1 (14) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P121/m1 (11) | <2; 3> | a, b, 2c | |
| P121/m1 (11) | <(2; 3) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] a' = 2a
| P121/a1 (14, P121/c1) | <3; 2 + (1, 0, 0)> | -2a - c, b, 2a | |
| P121/a1 (14, P121/c1) | <2; 3 + (1, 0, 0)> | -2a - c, b, 2a | 1/2, 0, 0 |
| P121/m1 (11) | <2; 3> | 2a, b, c | |
| P121/m1 (11) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] a' = 2a, c' = 2c
| B121/e1 (14, P121/c1) | <3; 2 + (0, 0, 1)> | a - c, b, 2c | |
| B121/e1 (14, P121/c1) | <2; 3 + (0, 0, 1)> | a - c, b, 2c | 0, 0, 1/2 |
| B121/m1 (11, P121/m1) | <2; 3> | a - c, b, 2c | |
| B121/m1 (11, P121/m1) | <(2; 3) + (0, 0, 1)> | a - c, b, 2c | 0, 0, 1/2 |
[3] b' = 3b
 | P121/m1 (11) | <3; 2 + (0, 1, 0)> | a, 3b, c | | | P121/m1 (11) | <2 + (0, 1, 0); 3 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P121/m1 (11) | <2 + (0, 1, 0); 3 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| P121/m1 (11) | <2; 3> | a, b, 3c | | | P121/m1 (11) | <(2; 3) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P121/m1 (11) | <(2; 3) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = a - c, c' = 3c
| P121/m1 (11) | <2; 3> | a - c, b, 3c | | | P121/m1 (11) | <(2; 3) + (0, 0, 2)> | a - c, b, 3c | 0, 0, 1 | | P121/m1 (11) | <(2; 3) + (0, 0, 4)> | a - c, b, 3c | 0, 0, 2 |
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[3] a' = a - 2c, c' = 3c
| P121/m1 (11) | <2; 3> | a - 2c, b, 3c | | | P121/m1 (11) | <(2; 3) + (0, 0, 2)> | a - 2c, b, 3c | 0, 0, 1 | | P121/m1 (11) | <(2; 3) + (0, 0, 4)> | a - 2c, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| P121/m1 (11) | <2; 3> | 3a, b, c | | | P121/m1 (11) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P121/m1 (11) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| P121/m1 (11) | <2 + (0, p/2 - 1/2, 0); 3 + (0, 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] a' = a - qc, c' = pc
| P121/m1 (11) | <(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 |
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[p] a' = pa
| P121/m1 (11) | <(2; 3) + (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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I Minimal translationengleiche supergroups
| [2] Pmma (51); [2] Pbcm (57); [2] Pmmn (59); [2] Pnma (62); [2] Cmcm (63); [3] P63/m (176) |
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) |
| [2] b' = 1/2b P12/m1 (10) |
