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) -y, -x, z | (8) -x + y, y, z | (9) x, x - y, z | | (10) -y, -x, -z | (11) -x + y, y, -z | (12) x, x - y, -z |
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I Maximal translationengleiche subgroups
| [2] P-611 (174, P-6) | 1; 2; 3; 4; 5; 6 |
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| [2] P3m1 (156) | 1; 2; 3; 7; 8; 9 |
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| [2] P312 (149) | 1; 2; 3; 10; 11; 12 |
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 | [3] Pmm2 (38, Amm2) | 1; 4; 7; 10 | c, -a - b, a - b
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| | [3] Pmm2 (38, Amm2) | 1; 4; 8; 11 | c, a, a + 2b
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| | [3] Pmm2 (38, Amm2) | 1; 4; 9; 12 | c, b, -2a - b
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P-6c2 (188) | <2; (4; 7) + (0, 0, 1)> | a, b, 2c | |
| P-6c2 (188) | <2; 4; 7 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P-6m2 (187) | <2; 4; 7> | a, b, 2c | |
| P-6m2 (187) | <2; 7; 4 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] c' = 3c
| P-6m2 (187) | <2; 4; 7> | a, b, 3c | | | P-6m2 (187) | <2; 7; 4 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P-6m2 (187) | <2; 7; 4 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a, b' = 3b
| H-6m2 (189, P-62m) | <2; 4; 7> | a - b, a + 2b, c | | | H-6m2 (189, P-62m) | <4; 2 + (1, -1, 0); 7 + (1, 1, 0)> | a - b, a + 2b, c | 1, 0, 0 | | H-6m2 (189, P-62m) | <4; 2 + (2, 1, 0); 7 + (2, 2, 0)> | a - b, a + 2b, c | 1, 1, 0 |
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| H-6m2 (189, P-62m) | <4; 2 + (1, 0, 0); 7 + (1, 1, 0)> | a - b, a + 2b, c | 2/3, 1/3, 0 | | H-6m2 (189, P-62m) | <4; (2; 7) + (2, 2, 0)> | a - b, a + 2b, c | 2/3, 4/3, 0 | | H-6m2 (189, P-62m) | <4; 2 + (3, 4, 0); 7 + (3, 3, 0)> | a - b, a + 2b, c | 2/3, 7/3, 0 |
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| H-6m2 (189, P-62m) | <4; (2; 7) + (1, 1, 0)> | a - b, a + 2b, c | 1/3, 2/3, 0 | | H-6m2 (189, P-62m) | <4; 2 + (2, 0, 0); 7 + (2, 2, 0)> | a - b, a + 2b, c | 4/3, 2/3, 0 | | H-6m2 (189, P-62m) | <4; 2 + (3, -1, 0); 7 + (3, 3, 0)> | a - b, a + 2b, c | 7/3, 2/3, 0 |
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[4] a' = 2a, b' = 2b
 | P-6m2 (187) | <2; 4; 7> | 2a, 2b, c | | | P-6m2 (187) | <4; 2 + (1, -1, 0); 7 + (1, 1, 0)> | 2a, 2b, c | 1, 0, 0 | | P-6m2 (187) | <4; 2 + (1, 2, 0); 7 + (1, 1, 0)> | 2a, 2b, c | 0, 1, 0 | | P-6m2 (187) | <4; 2 + (2, 1, 0); 7 + (2, 2, 0)> | 2a, 2b, c | 1, 1, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P-6m2 (187) | <2; 7; 4 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 1; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p2] a' = pa, b' = pb
| P-6m2 (187) | <4; 2 + (u + v, -u + 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
| [2] P6/mmm (191); [2] P63/mmc (194) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
