Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | |
| | (1) x, y, z | (2) -y, x - y, z + 1/3 | (3) -x + y, -x, z + 2/3 | | (4) y, x, -z | (5) x - y, -y, -z + 2/3 | (6) -x, -x + y, -z + 1/3 |
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I Maximal translationengleiche subgroups
| [2] P3111 (144, P31) | 1; 2; 3 |
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 | [3] P121 (5, C121) | 1; 4 | -a + b, -a - b, c
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| | [3] P121 (5, C121) | 1; 5 | -a - 2b, a, c
| 0, 0, 1/3
| | [3] P121 (5, C121) | 1; 6 | 2a + b, b, c
| 0, 0, 2/3
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P3221 (154) | <4; 2 + (0, 0, 1)> | a, b, 2c | |
| P3221 (154) | <(2; 4) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a, b' = 3b
| H3121 (151, P3112) | <2; 4> | a - b, a + 2b, c | 0, 0, 1/3 |
[4] a' = 2a, b' = 2b
 | P3121 (152) | <2; 4> | 2a, 2b, c | | | P3121 (152) | <(2; 4) + (1, -1, 0)> | 2a, 2b, c | 1, 0, 0 | | P3121 (152) | <2 + (1, 2, 0); 4 + (-1, 1, 0)> | 2a, 2b, c | 0, 1, 0 | | P3121 (152) | <4; 2 + (2, 1, 0)> | 2a, 2b, c | 1, 1, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P3221 (154) | <2 + (0, 0, 2p/3 - 1/3); 4 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 2 (mod 3) |
| P3121 (152) | <2 + (0, 0, p/3 - 1/3); 4 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 6; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 3) |
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[p2] a' = pa, b' = pb
| P3121 (152) | <2 + (u + v, -u + 2v, 0); 4 + (u - v, -u + v, 0)> | pa, pb, c | u, v, 0 | | | p > 1; p ≠ 3; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P6122 (178); [2] P6422 (181) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [3] H3121 (151, P3112); [3] R32 (obverse) (155, R32); [3] R32 (reverse) (155, R32) |
