Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3); (5)
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, -y, z | (3) y, -x, -z | (4) -y, x, -z | | (5) -x, y, -z | (6) x, -y, -z | (7) -y, -x, z | (8) y, x, z |
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I Maximal translationengleiche subgroups
| [2] I-411 (82, I-4) | (1; 2; 3; 4)+ |
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| [2] I21m (42, Fmm2) | (1; 2; 7; 8)+ | a - b, a + b, c
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| [2] I221 (23, I222) | (1; 2; 5; 6)+ |
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P-421c (114) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) | | |
| [2] P-421m (113) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) | | 0, 1/2, 1/4 |
| [2] P-42c (112) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) | | 0, 1/2, 1/4 |
| [2] P-42m (111) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
[3] c' = 3c
 | I-42m (121) | <2; 3; 5> | a, b, 3c | | | I-42m (121) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | I-42m (121) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| I-42m (121) | <2; (3; 5) + (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
| I-42m (121) | <2 + (2u, 2v, 0); 3 + (u - v, u + v, 0); 5 + (2u, 0, 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] I4/mmm (139); [2] I4/mcm (140); [3] I-43m (217) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C-42m (115, P-4m2) |
