Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z + 1/2 | (3) -y, x + 1/2, z + 1/4 | (4) y + 1/2, -x, z + 3/4 |
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I Maximal translationengleiche subgroups
| [2] I2 (5, A112) | (1; 2)+ | b, -a - b, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P43 (78) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | | 3/4, 3/4, 0 |
| [2] P41 (76) | 1; 2; 3; 4 | | 3/4, 1/4, 0 |
[3] c' = 3c
| I41 (80) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2)> | a, b, 3c | 1/2, 0, 0 |
- Series of maximal isomorphic subgroups
[p] c' = pc
| I41 (80) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/4 - 1/4)> | a, b, pc | | | | p > 4; p ≡ 1 (mod 4)
no conjugate subgroups |
| I41 (80) | <2 + (1, 0, p/2 - 1/2); 3 + (1/2, -1/2, p/4 - 1/4)> | a, b, pc | 1/2, 0, 0 | | | p > 2; p ≡ 3 (mod 4)
no conjugate subgroups |
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[p2] a' = pa, b' = pb
| I41 (80) | <2 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0); 3 + (u + v, p/2 - 1/2 - u + v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 3 (mod 4) |
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[p = q2 + r2] a' = qa - rb, b' = ra + qb
| I41 (80) | <2 + (q/2 + r/2 - 1/2 + 2u, -r/2 + q/2 - 1/2, 0); 3 + (r/2 + u, q/2 - u - 1/2, 0)> | qa - rb, ra + qb, c | u, 0, 0 | | | q > 0; r > 1; q odd; r even; p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
| I41 (80) | <2 + (q/2 + r/2 + 1/2 + 2u, -r/2 + q/2 - 1/2, 0); 3 + (r/2 + 1/2 + u, q/2 - 1 - u, 0)> | qa - rb, ra + qb, c | 1/2 + u, 0, 0 | | | q > 1; r > 0; q even; r odd; p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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I Minimal translationengleiche supergroups
| [2] I41/a (88); [2] I4122 (98); [2] I41md (109); [2] I41cd (110) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C42 (77, P42) |
