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) -x, -y, -z | (5) y, -x + y, -z | (6) x - y, x, -z |
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I Maximal translationengleiche subgroups
| [2] P3 (143) | 1; 2; 3 |
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| [3] P-1 (2) | 1; 4 |
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P-3 (147) | <2; 4> | a, b, 2c | |
| P-3 (147) | <2; 4 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] c' = 3c
 | P-3 (147) | <2; 4> | a, b, 3c | | | P-3 (147) | <2; 4 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P-3 (147) | <2; 4 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a, b' = 3b
| H-3 (147, P-3) | <2; 4> | a - b, a + 2b, c | | | H-3 (147, P-3) | <2 + (1, -1, 0); 4 + (2, 0, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H-3 (147, P-3) | <2 + (2, -2, 0); 4 + (4, 0, 0)> | a - b, a + 2b, c | 2, 0, 0 |
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[3] a' = a - b, b' = a + 2b, c' = 3c
| R-3 (148) | <2; 4> | a - b, a + 2b, 3c | | | R-3 (148) | <2; 4 + (0, 0, 2)> | a - b, a + 2b, 3c | 0, 0, 1 | | R-3 (148) | <2; 4 + (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-3 (148) | <2; 4> | 2a + b, -a + b, 3c | | | R-3 (148) | <2; 4 + (0, 0, 2)> | 2a + b, -a + b, 3c | 0, 0, 1 | | R-3 (148) | <2; 4 + (0, 0, 4)> | 2a + b, -a + b, 3c | 0, 0, 2 |
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[4] a' = 2a, b' = 2b
 | P-3 (147) | <2; 4> | 2a, 2b, c | | | P-3 (147) | <2 + (1, -1, 0); 4 + (2, 0, 0)> | 2a, 2b, c | 1, 0, 0 | | P-3 (147) | <2 + (1, 2, 0); 4 + (0, 2, 0)> | 2a, 2b, c | 0, 1, 0 | | P-3 (147) | <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
| P-3 (147) | <2; 4 + (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-3 (147) | <2 + (u + v, -u + 2v, 0); 4 + (2u, 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 1; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 2 (mod 3) |
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[p = q2 + r2 + qr] a' = qa - rb, b' = ra + (q + r)b
| P-3 (147) | <2 + (u, -u, 0); 4 + (2u, 0, 0)> | qa - rb, ra + (q + r)b, c | u, 0, 0 | | | q > 0; r > 0; p > 2; 0 ≤ u < p
p conjugate subgroups for each pair of q and r |
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I Minimal translationengleiche supergroups
| [2] P-31m (162); [2] P-31c (163); [2] P-3m1 (164); [2] P-3c1 (165); [2] P6/m (175); [2] P63/m (176) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [3] R-3 (obverse) (148, R-3); [3] R-3 (reverse) (148, R-3) |
