UNIQUE AXIS b, CELL CHOICE 1
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, -z + 1/2 | (3) -x, -y, -z | (4) x, -y, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] P1c1 (7) | 1; 4 |
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| [2] P121 (3) | 1; 2 |
| 0, 0, 1/4
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| [2] P-1 (2) | 1; 3 |
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II Maximal klassengleiche subgroups
[2] b' = 2b
| P121/c1 (14) | <3; 2 + (0, 1, 0)> | a, 2b, c | |
| P121/c1 (14) | <(2; 3) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
| P12/c1 (13) | <2; 3> | a, 2b, c | |
| P12/c1 (13) | <2; 3 + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] a' = 2a
| P12/c1 (13) | <2; 3> | 2a, b, c | |
| P12/c1 (13) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| P12/n1 (13, P12/c1) | <3; 2 + (1, 0, 0)> | 2a, b, -2a + c | |
| P12/n1 (13, P12/c1) | <2 + (2, 0, 0); 3 + (1, 0, 0)> | 2a, b, -2a + c | 1/2, 0, 0 |
[2] a' = 2a, b' = 2b
| C12/c1 (15) | <2; 3> | 2a, 2b, c | |
| C12/c1 (15) | <2; 3 + (0, 1, 0)> | 2a, 2b, c | 0, 1/2, 0 |
| C12/c1 (15) | <(2; 3) + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| C12/c1 (15) | <2 + (1, 0, 0); 3 + (1, 1, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
[3] b' = 3b
 | P12/c1 (13) | <2; 3> | a, 3b, c | | | P12/c1 (13) | <2; 3 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P12/c1 (13) | <2; 3 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| P12/c1 (13) | <3; 2 + (0, 0, 1)> | a, b, 3c | | | P12/c1 (13) | <2 + (0, 0, 3); 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P12/c1 (13) | <2 + (0, 0, 5); 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| P12/c1 (13) | <2; 3> | 3a, b, c | | | P12/c1 (13) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P12/c1 (13) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] a' = 3a, c' = -2a + c
| P12/c1 (13) | <3; 2 + (-1, 0, 0)> | 3a, b, -2a + c | | | P12/c1 (13) | <2 + (1, 0, 0); 3 + (2, 0, 0)> | 3a, b, -2a + c | 1, 0, 0 | | P12/c1 (13) | <2 + (3, 0, 0); 3 + (4, 0, 0)> | 3a, b, -2a + c | 2, 0, 0 |
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[3] a' = 3a, c' = -4a + c
| P12/c1 (13) | <3; 2 + (-2, 0, 0)> | 3a, b, -4a + c | | | P12/c1 (13) | <2 + (0, 0, 0); 3 + (2, 0, 0)> | 3a, b, -4a + c | 1, 0, 0 | | P12/c1 (13) | <2 + (2, 0, 0); 3 + (4, 0, 0)> | 3a, b, -4a + c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| P12/c1 (13) | <2; 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] c' = pc
| P12/c1 (13) | <2 + (0, 0, p/2 - 1/2 + 2u); 3 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] a' = pa, c' = -2qa + c
| P12/c1 (13) | <2 + (-q + 2u, 0, 0); 3 + (2u, 0, 0)> | pa, b, -2qa + c | u, 0, 0 | | | p > 2; 0 ≤ q < p; 0 ≤ u < p
p conjugate subgroups for each pair of q and prime p |
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I Minimal translationengleiche supergroups
| [2] Pnnn (48); [2] Pccm (49); [2] Pban (50); [2] Pmma (51); [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pccn (56); [2] Pbcm (57); [2] Pmmn (59); [2] Pbcn (60); [2] Cmme (67); [2] Ccce (68); [2] P4/n (85); [2] P42/n (86) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A12/m1 (12, C12/m1); [2] C12/c1 (15); [2] I12/c1 (15, C12/c1) |
| [2] c' = 1/2c P12/m1 (10) |
