ORIGIN CHOICE 1, Origin at 2 2 2, at 1/4, 1/4, 1/4 from -1
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z | | (5) -x + 1/2, -y + 1/2, -z + 1/2 | (6) x + 1/2, y + 1/2, -z + 1/2 | (7) x + 1/2, -y + 1/2, z + 1/2 | (8) -x + 1/2, y + 1/2, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] Pnn2 (34) | 1; 2; 7; 8 |
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| [2] Pn2n (34, Pnn2) | 1; 3; 6; 8 | c, a, b
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| [2] P2nn (34, Pnn2) | 1; 4; 6; 7 | b, c, a
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| [2] P222 (16) | 1; 2; 3; 4 |
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| [2] P112/n (13, P112/a) | 1; 2; 5; 6 | -a - b, a, c
| 1/4, 1/4, 1/4
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| [2] P12/n1 (13, P12/c1) | 1; 3; 5; 7 | c, b, -a - c
| 1/4, 1/4, 1/4
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| [2] P2/n11 (13, P12/c1) | 1; 4; 5; 8 | -b, a, b + c
| 1/4, 1/4, 1/4
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| Fddd (70) | <2; 3; 5> | 2a, 2b, 2c | |
| Fddd (70) | <2; (3; 5) + (0, 0, 1)> | 2a, 2b, 2c | 0, 0, 1/2 |
| Fddd (70) | <(2; 3; 5) + (0, 0, 1)> | 2a, 2b, 2c | 1/2, 0, 0 |
| Fddd (70) | <3; (2; 5) + (0, 0, 1)> | 2a, 2b, 2c | 0, 1/2, 0 |
| Fddd (70) | <2; 5; 3 + (0, 0, 1)> | 2a, 2b, 2c | 1/2, 1/2, 0 |
| Fddd (70) | <3; 5; 2 + (0, 0, 1)> | 2a, 2b, 2c | 1/2, 0, 1/2 |
| Fddd (70) | <5; (2; 3) + (0, 0, 1)> | 2a, 2b, 2c | 0, 1/2, 1/2 |
| Fddd (70) | <2; 3; 5 + (0, 0, 1)> | 2a, 2b, 2c | 1/2, 1/2, 1/2 |
[3] a' = 3a
 | Pnnn (48) | <2; 3; 5 + (1, 0, 0)> | 3a, b, c | | | Pnnn (48) | <(2; 3) + (2, 0, 0); 5 + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pnnn (48) | <(2; 3) + (4, 0, 0); 5 + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pnnn (48) | <2; 3; 5 + (0, 1, 0)> | a, 3b, c | | | Pnnn (48) | <3; 2 + (0, 2, 0); 5 + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Pnnn (48) | <3; 2 + (0, 4, 0); 5 + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pnnn (48) | <2; 3; 5 + (0, 0, 1)> | a, b, 3c | | | Pnnn (48) | <2; 3 + (0, 0, 2); 5 + (0, 0, 3)> | a, b, 3c | 0, 0, 1 | | Pnnn (48) | <2; 3 + (0, 0, 4); 5 + (0, 0, 5)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pnnn (48) | <(2; 3) + (2u, 0, 0); 5 + (p/2 - 1/2 + 2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] b' = pb
| Pnnn (48) | <3; 2 + (0, 2u, 0); 5 + (0, p/2 - 1/2 + 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| Pnnn (48) | <2; 3 + (0, 0, 2u); 5 + (0, 0, p/2 - 1/2 + 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P4/nnc (126); [2] P42/nnm (134); [3] Pn-3 (201) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Immm (71); [2] Amaa (66, Cccm); [2] Bbmb (66, Cccm); [2] Cccm (66) |
| [2] a' = 1/2a Pncb (50, Pban); [2] b' = 1/2b Pcna (50, Pban); [2] c' = 1/2c Pban (50) |
