Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z + 1/2 | (3) -x, y + 1/2, -z + 1/2 | (4) x, -y + 1/2, -z | | (5) -x, -y, -z | (6) x, y, -z + 1/2 | (7) x, -y + 1/2, z + 1/2 | (8) -x, y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] Pbc21 (29, Pca21) | 1; 2; 7; 8 | -b, a, c
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| [2] P2cm (28, Pma2) | 1; 4; 6; 7 | c, b, -a
| 0, 1/4, 0
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| [2] Pb21m (26, Pmc21) | 1; 3; 6; 8 | c, a, b
| 0, 0, 1/4
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| [2] P22121 (18, P21212) | 1; 2; 3; 4 | b, c, a
| 0, 1/4, 0
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| [2] P121/c1 (14) | 1; 3; 5; 7 |
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| [2] P2/b11 (13, P12/c1) | 1; 4; 5; 8 | c, a, b
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| [2] P1121/m (11, P1121/m) | 1; 2; 5; 6 |
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II Maximal klassengleiche subgroups
[2] a' = 2a
| Pbnm (62, Pnma) | <2; 5; 3 + (1, 0, 0)> | b, c, 2a | |
| Pbnm (62, Pnma) | <3; (2; 5) + (1, 0, 0)> | b, c, 2a | 1/2, 0, 0 |
| Pbca (61) | <3; 5; 2 + (1, 0, 0)> | 2a, b, c | |
| Pbca (61) | <2; (3; 5) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| Pbna (60, Pbcn) | <5; (2; 3) + (1, 0, 0)> | c, 2a, b | |
| Pbna (60, Pbcn) | <2; 3; 5 + (1, 0, 0)> | c, 2a, b | 1/2, 0, 0 |
| Pbcm (57) | <2; 3; 5> | 2a, b, c | |
| Pbcm (57) | <(2; 3; 5) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[3] a' = 3a
 | Pbcm (57) | <2; 3; 5> | 3a, b, c | | | Pbcm (57) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pbcm (57) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pbcm (57) | <2; 5; 3 + (0, 1, 0)> | a, 3b, c | | | Pbcm (57) | <(2; 5) + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | Pbcm (57) | <(2; 5) + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pbcm (57) | <5; (2; 3) + (0, 0, 1)> | a, b, 3c | | | Pbcm (57) | <2 + (0, 0, 1); 3 + (0, 0, 3); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pbcm (57) | <2 + (0, 0, 1); 3 + (0, 0, 5); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pbcm (57) | <(2; 3; 5) + (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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[p] b' = pb
| Pbcm (57) | <(2; 5) + (0, 2u, 0); 3 + (0, p/2 - 1/2, 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
| Pbcm (57) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/2 - 1/2 + 2u); 5 + (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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I Minimal translationengleiche supergroups
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Cmcm (63); [2] Bbem (64, Cmce); [2] Aemm (67, Cmme); [2] Ibam (72) |
| [2] b' = 1/2b Pmcm (51, Pmma); [2] c' = 1/2c Pbmm (51, Pmma) |
