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) -y, -x, -z + 1/2 | (5) -x + y, y, -z + 1/2 | (6) x, x - y, -z + 1/2 | | (7) -x, -y, -z | (8) y, -x + y, -z | (9) x - y, x, -z | | (10) y, x, z + 1/2 | (11) x - y, -y, z + 1/2 | (12) -x, -x + y, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] P31c (159) | 1; 2; 3; 10; 11; 12 |
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| [2] P312 (149) | 1; 2; 3; 4; 5; 6 |
| 0, 0, 1/4
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| [2] P-311 (147, P-3) | 1; 2; 3; 7; 8; 9 |
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 | [3] P112/c (15, C12/c1) | 1; 4; 7; 10 | -a - b, a - b, c
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| | [3] P112/c (15, C12/c1) | 1; 5; 7; 11 | a, a + 2b, c
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| | [3] P112/c (15, C12/c1) | 1; 6; 7; 12 | b, -2a - b, c
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II Maximal klassengleiche subgroups
[3] c' = 3c
| P-31c (163) | <2; 7; 4 + (0, 0, 1)> | a, b, 3c | | | P-31c (163) | <2; 4 + (0, 0, 3); 7 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P-31c (163) | <2; 4 + (0, 0, 5); 7 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a, b' = 3b
| H-31c (165, P-3c1) | <2; 4; 7> | a - b, a + 2b, c | | | H-31c (165, P-3c1) | <2 + (1, -1, 0); 4 + (1, 1, 0); 7 + (2, 0, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H-31c (165, P-3c1) | <2 + (2, 1, 0); (4; 7) + (2, 2, 0)> | a - b, a + 2b, c | 1, 1, 0 |
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[3] a' = a - b, b' = a + 2b, c' = 3c
| R-3c (167) | <2; 7; 4 + (0, 0, 1)> | a - b, a + 2b, 3c | | | R-3c (167) | <2; 4 + (0, 0, 3); 7 + (0, 0, 2)> | a - b, a + 2b, 3c | 0, 0, 1 | | R-3c (167) | <2; 4 + (0, 0, 5); 7 + (0, 0, 4)> | a - b, a + 2b, 3c | 0, 0, 2 |
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[3] a' = 2a + b, b' = -a + b, c' = 3c
| R-3c (167) | <2; 7; 4 + (0, 0, 1)> | 2a + b, -a + b, 3c | | | R-3c (167) | <2; 4 + (0, 0, 3); 7 + (0, 0, 2)> | 2a + b, -a + b, 3c | 0, 0, 1 | | R-3c (167) | <2; 4 + (0, 0, 5); 7 + (0, 0, 4)> | 2a + b, -a + b, 3c | 0, 0, 2 |
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[4] a' = 2a, b' = 2b
 | P-31c (163) | <2; 4; 7> | 2a, 2b, c | | | P-31c (163) | <2 + (1, -1, 0); 4 + (1, 1, 0); 7 + (2, 0, 0)> | 2a, 2b, c | 1, 0, 0 | | P-31c (163) | <2 + (1, 2, 0); 4 + (1, 1, 0); 7 + (0, 2, 0)> | 2a, 2b, c | 0, 1, 0 | | P-31c (163) | <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
| P-31c (163) | <2; 4 + (0, 0, p/2 - 1/2 + 2u); 7 + (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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[p2] a' = pa, b' = pb
| P-31c (163) | <2 + (u + v, -u + 2v, 0); 4 + (u + v, u + v, 0); 7 + (2u, 2v, 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] P6/mcc (192); [2] P63/mmc (194) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c P-31m (162) |
