Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x, -y + 1/2, z | (3) -x, y + 1/2, -z | (4) x, -y, -z | | (5) -x, -y, -z | (6) x, y + 1/2, -z | (7) x, -y + 1/2, z | (8) -x, y, z |
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I Maximal translationengleiche subgroups
| [2] Cm2e (39, Aem2) | (1; 3; 6; 8)+ | c, a, b
| 1/4, 0, 0
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| [2] C2me (39, Aem2) | (1; 4; 6; 7)+ | c, b, -a
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| [2] Cmm2 (35) | (1; 2; 7; 8)+ |
| 0, 1/4, 0
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| [2] C222 (21) | (1; 2; 3; 4)+ |
| 1/4, 0, 0
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| [2] C112/e (13, P112/a) | (1; 2; 5; 6)+ | a, 1/2(-a + b), c
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| [2] C12/m1 (12) | (1; 3; 5; 7)+ |
| 1/4, 1/4, 0
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| [2] C2/m11 (12, C12/m1) | (1; 4; 5; 8)+ | -b, a, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pbma (57, Pbcm) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 0) | c, a, b | |
| [2] Pmab (57, Pbcm) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 0) | c, b, -a | 1/4, 1/4, 0 |
| [2] Pbaa (54, Pcca) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 0) | b, c, a | 1/4, 1/4, 0 |
| [2] Pbab (54, Pcca) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 0) | a, -c, b | |
| [2] Pmmb (51, Pmma) | 1; 2; 3; 4; 5; 6; 7; 8 | -b, a, c | |
| [2] Pmma (51) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] Pmaa (49, Pccm) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 0) | b, c, a | |
| [2] Pbmb (49, Pccm) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 0) | c, a, b | 1/4, 1/4, 0 |
[2] c' = 2c
| Imma (74) | <2; 3; 5> | a, b, 2c | |
| Imma (74) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Ibca (73) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Ibca (73) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Ibmb (72, Ibam) | <3; 5; 2 + (0, 0, 1)> | 2c, a, b | 1/4, 1/4, 1/2 |
| Ibmb (72, Ibam) | <(2; 3; 5) + (0, 0, 1)> | 2c, a, b | 1/4, 1/4, 0 |
| Imaa (72, Ibam) | <5; (2; 3) + (0, 0, 1)> | b, 2c, a | |
| Imaa (72, Ibam) | <3; (2; 5) + (0, 0, 1)> | b, 2c, a | 0, 0, 1/2 |
| Ccce (68) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | 1/4, 1/4, 0 |
| Ccce (68) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 1/4, 1/4, 1/2 |
| Cmme (67) | <2; 3; 5> | a, b, 2c | |
| Cmme (67) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Ccme (64, Cmce) | <3; 5; 2 + (0, 0, 1)> | -b, a, 2c | 1/4, 1/4, 0 |
| Ccme (64, Cmce) | <(2; 3; 5) + (0, 0, 1)> | -b, a, 2c | 1/4, 1/4, 1/2 |
| Cmce (64) | <5; (2; 3) + (0, 0, 1)> | a, b, 2c | |
| Cmce (64) | <3; (2; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a
 | Cmme (67) | <2; 3; 5> | 3a, b, c | | | Cmme (67) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Cmme (67) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Cmme (67) | <5; (2; 3) + (0, 1, 0)> | a, 3b, c | | | Cmme (67) | <2 + (0, 3, 0); 3 + (0, 1, 0); 5 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Cmme (67) | <2 + (0, 5, 0); 3 + (0, 1, 0); 5 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Cmme (67) | <2; 3; 5> | a, b, 3c | | | Cmme (67) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Cmme (67) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Cmme (67) | <(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
| Cmme (67) | <2 + (0, p/2 - 1/2 + 2u, 0); 3 + (0, p/2 - 1/2, 0); 5 + (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
| Cmme (67) | <2; (3; 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
| [2] P4/nbm (125); [2] P4/nmm (129); [2] P42/nnm (134); [2] P42/ncm (138) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b Pmmm (47) |
