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-4 (82) | (1; 2; 7; 8)+ |
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| [2] I4 (79) | (1; 2; 3; 4)+ |
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| [2] I2/m (12, A112/m) | (1; 2; 5; 6)+ | b, -a - b, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P42/n (86) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] P4/n (85) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] P42/m (84) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) | | 0, 1/2, 0 |
| [2] P4/m (83) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
[3] c' = 3c
 | I4/m (87) | <2; 3; 5> | a, b, 3c | | | I4/m (87) | <2; 3; 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | I4/m (87) | <2; 3; 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| I4/m (87) | <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
| I4/m (87) | <(2; 5) + (2u, 2v, 0); 3 + (u + v, -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
| I4/m (87) | <(2; 5) + (2u, 0, 0); 3 + (u, -u, 0)> | qa - rb, ra + qb, c | u, 0, 0 | | | q > 0; r > 0; p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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I Minimal translationengleiche supergroups
| [2] I4/mmm (139); [2] I4/mcm (140) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C4/m (83, P4/m) |
