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 | (5) y, -x + y, z | (6) x - y, x, z | | (7) -x, -y, -z | (8) y, -x + y, -z | (9) x - y, x, -z | | (10) x, y, -z | (11) -y, x - y, -z | (12) -x + y, -x, -z |
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I Maximal translationengleiche subgroups
| [2] P-6 (174) | 1; 2; 3; 10; 11; 12 |
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| [2] P6 (168) | 1; 2; 3; 4; 5; 6 |
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| [2] P-3 (147) | 1; 2; 3; 7; 8; 9 |
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| [3] P2/m (10, P112/m) | 1; 4; 7; 10 |
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P63/m (176) | <2; 7; 4 + (0, 0, 1)> | a, b, 2c | |
| P63/m (176) | <2; (4; 7) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P6/m (175) | <2; 4; 7> | a, b, 2c | |
| P6/m (175) | <2; 4; 7 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] c' = 3c
 | P6/m (175) | <2; 4; 7> | a, b, 3c | | | P6/m (175) | <2; 4; 7 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P6/m (175) | <2; 4; 7 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a, b' = 3b
| H6/m (175, P6/m) | <2; 4; 7> | a - b, a + 2b, c | | | H6/m (175, P6/m) | <2 + (1, -1, 0); (4; 7) + (2, 0, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H6/m (175, P6/m) | <2 + (2, -2, 0); (4; 7) + (4, 0, 0)> | a - b, a + 2b, c | 2, 0, 0 |
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[4] a' = 2a, b' = 2b
 | P6/m (175) | <2; 4; 7> | 2a, 2b, c | | | P6/m (175) | <2 + (1, -1, 0); (4; 7) + (2, 0, 0)> | 2a, 2b, c | 1, 0, 0 | | P6/m (175) | <2 + (1, 2, 0); (4; 7) + (0, 2, 0)> | 2a, 2b, c | 0, 1, 0 | | P6/m (175) | <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
| P6/m (175) | <2; 4; 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
| P6/m (175) | <2 + (u + v, -u + 2v, 0); (4; 7) + (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
| P6/m (175) | <2 + (u, -u, 0); (4; 7) + (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] P6/mmm (191); [2] P6/mcc (192) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
