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) -y, x, z + 1/2 | (4) y, -x, z + 1/2 | | (5) x, -y, z + 1/2 | (6) -x, y, z + 1/2 | (7) -y, -x, z | (8) y, x, z |
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I Maximal translationengleiche subgroups
| [2] P4211 (77, P42) | 1; 2; 3; 4 |
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| [2] P21m (35, Cmm2) | 1; 2; 7; 8 | a - b, a + b, c
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| [2] P2c1 (27, Pcc2) | 1; 2; 5; 6 |
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b
| C42cd (106, P42bc) | <2; 3; 5 + (0, 1, 0)> | a - b, a + b, c | |
| C42cd (106, P42bc) | <2; 5; 3 + (1, 0, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
| C42cm (105, P42mc) | <2; 3; 5> | a - b, a + b, c | |
| C42cm (105, P42mc) | <2; 3 + (1, 0, 0); 5 + (0, 1, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
[3] c' = 3c
| P42cm (101) | <2; (3; 5) + (0, 0, 1)> | a, b, 3c | |
- Series of maximal isomorphic subgroups
[p] c' = pc
| P42cm (101) | <2; (3; 5) + (0, 0, p/2 - 1/2)> | a, b, pc | | | | p > 2
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| P42cm (101) | <2 + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (0, 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P42/mcm (132); [2] P42/ncm (138) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C42cm (105, P42mc); [2] I4cm (108) |
