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 + 1/2 | (3) -y, x, z + 1/4 | (4) y, -x, z + 3/4 | | (5) -x, y, -z | (6) x, -y, -z + 1/2 | (7) y, x, -z + 3/4 | (8) -y, -x, -z + 1/4 |
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I Maximal translationengleiche subgroups
| [2] P4111 (76, P41) | 1; 2; 3; 4 |
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| [2] P2121 (17, P2221) | 1; 2; 5; 6 |
| 0, 0, 1/4
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| [2] P2112 (20, C2221) | 1; 2; 7; 8 | a - b, a + b, c
| 0, 0, 1/8
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b
| C41221 (92, P41212) | <2; 3; 5 + (1, 0, 0)> | a - b, a + b, c | 1/2, 1/2, 1/4 |
| C41221 (92, P41212) | <2; 5; 3 + (1, 0, 0)> | a - b, a + b, c | 0, 0, 1/4 |
| C4122 (91, P4122) | <2; 3; 5 + (0, 0, 1)> | a - b, a + b, c | 0, 0, 3/8 |
| C4122 (91, P4122) | <2 + (1, 1, 0); 3 + (1, 0, 0); 5 + (1, 0, 1)> | a - b, a + b, c | 1/2, 1/2, 3/8 |
[3] c' = 3c
 | P4322 (95) | <5; 2 + (0, 0, 1); 3 + (0, 0, 2)> | a, b, 3c | | | P4322 (95) | <2 + (0, 0, 1); (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P4322 (95) | <2 + (0, 0, 1); 3 + (0, 0, 2); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P4322 (95) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, 3p/4 - 1/4); 5 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| P4122 (91) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/4 - 1/4); 5 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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[p2] a' = pa, b' = pb
| P4122 (91) | <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
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
