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 + 1/3 | (3) -x + y, -x, z + 2/3 | | (4) -x, -y, z + 1/2 | (5) y, -x + y, z + 5/6 | (6) x - y, x, z + 1/6 | | (7) y, x, -z + 1/3 | (8) x - y, -y, -z | (9) -x, -x + y, -z + 2/3 | | (10) -y, -x, -z + 5/6 | (11) -x + y, y, -z + 1/2 | (12) x, x - y, -z + 1/6 |
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I Maximal translationengleiche subgroups
| [2] P6111 (169, P61) | 1; 2; 3; 4; 5; 6 |
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| [2] P3121 (152) | 1; 2; 3; 7; 8; 9 |
| 0, 0, 1/6
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| [2] P3112 (151) | 1; 2; 3; 10; 11; 12 |
| 0, 0, 1/12
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 | [3] P2122 (20, C2221) | 1; 4; 7; 10 | -a + b, -a - b, c
| 0, 0, 5/12
| | [3] P2122 (20, C2221) | 1; 4; 8; 11 | -a - 2b, a, c
| 0, 0, 3/4
| | [3] P2122 (20, C2221) | 1; 4; 9; 12 | 2a + b, b, c
| 0, 0, 1/12
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II Maximal klassengleiche subgroups
[3] a' = 3a, b' = 3b
| H6122 (178, P6122) | <2; 4; 7 + (0, 0, 1)> | a - b, a + 2b, c | 0, 0, 5/12 | | H6122 (178, P6122) | <2 + (1, -1, 0); 4 + (2, 0, 0); 7 + (1, -1, 1)> | a - b, a + 2b, c | 1, 0, 5/12 | | H6122 (178, P6122) | <2 + (2, -2, 0); 4 + (4, 0, 0); 7 + (2, -2, 1)> | a - b, a + 2b, c | 2, 0, 5/12 |
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[4] a' = 2a, b' = 2b
 | P6122 (178) | <2; 4; 7> | 2a, 2b, c | | | P6122 (178) | <(2; 7) + (1, -1, 0); 4 + (2, 0, 0)> | 2a, 2b, c | 1, 0, 0 | | P6122 (178) | <2 + (1, 2, 0); 4 + (0, 2, 0); 7 + (-1, 1, 0)> | 2a, 2b, c | 0, 1, 0 | | P6122 (178) | <7; 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
| P6522 (179) | <2 + (0, 0, 2p/3 - 1/3); 4 + (0, 0, p/2 - 1/2); 7 + (0, 0, 2p/3 - 1/3 + 2u)> | a, b, pc | 0, 0, u | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 5 (mod 6) |
| P6122 (178) | <2 + (0, 0, p/3 - 1/3); 4 + (0, 0, p/2 - 1/2); 7 + (0, 0, p/3 - 1/3 + 2u)> | a, b, pc | 0, 0, u | | | p > 6; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 6) |
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[p2] a' = pa, b' = pb
| P6122 (178) | <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
| [2] c' = 1/2c P6222 (180); [3] c' = 1/3c P6322 (182) |
