Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)
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 |
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I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] c' = 2c
| P32 (145) | <2 + (0, 0, 1)> | a, b, 2c | |
[3] a' = 3a, b' = 3b
| H31 (144, P31) | <2> | a - b, a + 2b, c | |
| H31 (144, P31) | <2 + (1, 0, 0)> | a - b, a + 2b, c | 2/3, 1/3, 0 |
| H31 (144, P31) | <2 + (1, 1, 0)> | a - b, a + 2b, c | 1/3, 2/3, 0 |
[4] a' = 2a, b' = 2b
 | P31 (144) | <2> | 2a, 2b, c | | | P31 (144) | <2 + (1, -1, 0)> | 2a, 2b, c | 1, 0, 0 | | P31 (144) | <2 + (1, 2, 0)> | 2a, 2b, c | 0, 1, 0 | | P31 (144) | <2 + (2, 1, 0)> | 2a, 2b, c | 1, 1, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P32 (145) | <2 + (0, 0, 2p/3 - 1/3)> | a, b, pc | | | | p > 1; p ≡ 2 (mod 3)
no conjugate subgroups |
| P31 (144) | <2 + (0, 0, p/3 - 1/3)> | a, b, pc | | | | p > 6; p ≡ 1 (mod 3)
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| P31 (144) | <2 + (u + v, -u + 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 1; p ≡ 2 (mod 3); 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
| P31 (144) | <2 + (u, -u, 0)> | qa - rb, ra + (q + r)b, c | u, 0, 0 | | | q > 0; r > 0; p > 6; 0 ≤ u < p
p conjugate subgroups for each pair of q and r |
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I Minimal translationengleiche supergroups
| [2] P3112 (151); [2] P3121 (152); [2] P61 (169); [2] P64 (172) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [3] R3 (obverse) (146, R3); [3] R3 (reverse) (146, R3) |
