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 | (3) -x + y, -x, z | | (4) -y, -x, z | (5) -x + y, y, z | (6) x, x - y, z |
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I Maximal translationengleiche subgroups
| [2] P311 (143, P3) | 1; 2; 3 |
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 | [3] P1m1 (8, C1m1) | 1; 4 | -a + b, -a - b, c
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| | [3] P1m1 (8, C1m1) | 1; 5 | -a - 2b, a, c
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| | [3] P1m1 (8, C1m1) | 1; 6 | 2a + b, b, c
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P3c1 (158) | <2; 4 + (0, 0, 1)> | a, b, 2c | |
| P3m1 (156) | <2; 4> | a, b, 2c | |
[3] c' = 3c
[3] a' = 3a, b' = 3b
| H3m1 (157, P31m) | <2; 4> | a - b, a + 2b, c | | | H3m1 (157, P31m) | <2 + (1, -1, 0); 4 + (1, 1, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H3m1 (157, P31m) | <2 + (2, 1, 0); 4 + (2, 2, 0)> | a - b, a + 2b, c | 1, 1, 0 |
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| H3m1 (157, P31m) | <4; 2 + (1, 0, 0)> | a - b, a + 2b, c | 2/3, -2/3, 0 | | H3m1 (157, P31m) | <2 + (2, 2, 0); 4 + (1, 1, 0)> | a - b, a + 2b, c | 2/3, 1/3, 0 | | H3m1 (157, P31m) | <2 + (3, 4, 0); 4 + (2, 2, 0)> | a - b, a + 2b, c | 2/3, 4/3, 0 |
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| H3m1 (157, P31m) | <4; 2 + (1, 1, 0)> | a - b, a + 2b, c | 1/3, -1/3, 0 | | H3m1 (157, P31m) | <2 + (2, 3, 0); 4 + (1, 1, 0)> | a - b, a + 2b, c | 1/3, 2/3, 0 | | H3m1 (157, P31m) | <2 + (3, 2, 0); 4 + (2, 2, 0)> | a - b, a + 2b, c | 4/3, 2/3, 0 |
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[4] a' = 2a, b' = 2b
 | P3m1 (156) | <2; 4> | 2a, 2b, c | | | P3m1 (156) | <2 + (1, -1, 0); 4 + (1, 1, 0)> | 2a, 2b, c | 1, 0, 0 | | P3m1 (156) | <2 + (1, 2, 0); 4 + (1, 1, 0)> | 2a, 2b, c | 0, 1, 0 | | P3m1 (156) | <2 + (2, 1, 0); 4 + (2, 2, 0)> | 2a, 2b, c | 1, 1, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P3m1 (156) | <2; 4> | a, b, pc | | | | p > 1
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| P3m1 (156) | <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] P-3m1 (164); [2] P6mm (183); [2] P63mc (186); [2] P-6m2 (187) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [3] H3m1 (157, P31m); [3] R3m (obverse) (160, R3m); [3] R3m (reverse) (160, R3m) |
