Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4); (7)
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) -x, -y, z + 1/2 | (5) y, -x + y, z + 1/2 | (6) x - y, x, z + 1/2 | | (7) -y, -x, z + 1/2 | (8) -x + y, y, z + 1/2 | (9) x, x - y, z + 1/2 | | (10) y, x, z | (11) x - y, -y, z | (12) -x, -x + y, z |
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I Maximal translationengleiche subgroups
| [2] P6311 (173, P63) | 1; 2; 3; 4; 5; 6 |
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| [2] P3c1 (158) | 1; 2; 3; 7; 8; 9 |
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| [2] P31m (157) | 1; 2; 3; 10; 11; 12 |
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 | [3] P21cm (36, Cmc21) | 1; 4; 7; 10 | -a + b, -a - b, c
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| | [3] P21cm (36, Cmc21) | 1; 4; 8; 11 | -a - 2b, a, c
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| | [3] P21cm (36, Cmc21) | 1; 4; 9; 12 | 2a + b, b, c
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II Maximal klassengleiche subgroups
[3] c' = 3c
| P63cm (185) | <2; (4; 7) + (0, 0, 1)> | a, b, 3c | |
[3] a' = 3a, b' = 3b
| H63cm (186, P63mc) | <2; 4; 7> | a - b, a + 2b, c | | | H63cm (186, P63mc) | <2 + (1, -1, 0); 4 + (2, 0, 0); 7 + (1, 1, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H63cm (186, P63mc) | <2 + (2, 1, 0); (4; 7) + (2, 2, 0)> | a - b, a + 2b, c | 1, 1, 0 |
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[4] a' = 2a, b' = 2b
 | P63cm (185) | <2; 4; 7> | 2a, 2b, c | | | P63cm (185) | <2 + (1, -1, 0); 4 + (2, 0, 0); 7 + (1, 1, 0)> | 2a, 2b, c | 1, 0, 0 | | P63cm (185) | <2 + (1, 2, 0); 4 + (0, 2, 0); 7 + (1, 1, 0)> | 2a, 2b, c | 0, 1, 0 | | P63cm (185) | <2 + (2, 1, 0); (4; 7) + (2, 2, 0)> | 2a, 2b, c | 1, 1, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P63cm (185) | <2; (4; 7) + (0, 0, p/2 - 1/2)> | a, b, pc | | | | p > 2
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| P63cm (185) | <2 + (u + v, -u + 2v, 0); 4 + (2u, 2v, 0); 7 + (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
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
