Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y, z + 1/2 | (3) -x, y + 1/2, -z + 1/2 | (4) x + 1/2, -y + 1/2, -z | | (5) -x, -y, -z | (6) x + 1/2, y, -z + 1/2 | (7) x, -y + 1/2, z + 1/2 | (8) -x + 1/2, y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] Ibc2 (45, Iba2) | (1; 2; 7; 8)+ |
| 0, 1/4, 0
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| [2] Ib2a (45, Iba2) | (1; 3; 6; 8)+ | c, a, b
| 1/4, 0, 0
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| [2] I2ca (45, Iba2) | (1; 4; 6; 7)+ | b, c, a
| 0, 0, 1/4
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| [2] I212121 (24) | (1; 2; 3; 4)+ |
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| [2] I112/a (15, A112/a) | (1; 2; 5; 6)+ | b, -a - b, c
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| [2] I12/c1 (15, C12/c1) | (1; 3; 5; 7)+ | -a - c, b, a
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| [2] I2/b11 (15, C12/c1) | (1; 4; 5; 8)+ | -b - c, a, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pbca (61) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
| [2] Pcab (61, Pbca) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) | -b, a, c | 1/4, 1/4, 1/4 |
| [2] Pcaa (54, Pcca) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) | c, b, -a | |
| [2] Pccb (54, Pcca) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 1/2) | -b, a, c | |
| [2] Pbab (54, Pcca) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 1/2) | a, -c, b | |
| [2] Pbcb (54, Pcca) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) | c, a, b | 1/4, 1/4, 1/4 |
| [2] Pbaa (54, Pcca) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 1/2) | b, c, a | 1/4, 1/4, 1/4 |
| [2] Pcca (54) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
[3] a' = 3a
 | Ibca (73) | <3; 5; 2 + (1, 0, 0)> | 3a, b, c | | | Ibca (73) | <2 + (3, 0, 0); (3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Ibca (73) | <2 + (5, 0, 0); (3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Ibca (73) | <2; 5; 3 + (0, 1, 0)> | a, 3b, c | | | Ibca (73) | <(2; 5) + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | Ibca (73) | <(2; 5) + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Ibca (73) | <5; (2; 3) + (0, 0, 1)> | a, b, 3c | | | Ibca (73) | <2 + (0, 0, 1); 3 + (0, 0, 3); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Ibca (73) | <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
| Ibca (73) | <2 + (p/2 - 1/2 + 2u, 0, 0); (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
| Ibca (73) | <(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
| Ibca (73) | <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
| [2] I41/acd (142); [2] Ia-3 (206) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a Aemm (67, Cmme); [2] b' = 1/2b Bmem (67, Cmme); [2] c' = 1/2c Cmme (67) |
