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) -x + 1/2, y + 1/2, -z + 1/2 | (4) x + 1/2, -y + 1/2, -z + 1/2 | | (5) -x, -y, -z | (6) x, y, -z | (7) x + 1/2, -y + 1/2, z + 1/2 | (8) -x + 1/2, y + 1/2, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] Pnn2 (34) | 1; 2; 7; 8 |
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| [2] Pn21m (31, Pmn21) | 1; 3; 6; 8 | c, a, b
| 1/4, 0, 0
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| [2] P21nm (31, Pmn21) | 1; 4; 6; 7 | -c, b, a
| 0, 1/4, 0
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| [2] P21212 (18) | 1; 2; 3; 4 |
| 0, 0, 1/4
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| [2] P121/n1 (14, P121/c1) | 1; 3; 5; 7 | c, b, -a - c
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| [2] P21/n11 (14, P121/c1) | 1; 4; 5; 8 | -c, a, b + c
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| [2] P112/m (10) | 1; 2; 5; 6 |
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II Maximal klassengleiche subgroups
[3] a' = 3a
 | Pnnm (58) | <2; 5; 3 + (1, 0, 0)> | 3a, b, c | | | Pnnm (58) | <(2; 5) + (2, 0, 0); 3 + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pnnm (58) | <(2; 5) + (4, 0, 0); 3 + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pnnm (58) | <2; 5; 3 + (0, 1, 0)> | a, 3b, c | | | Pnnm (58) | <(2; 5) + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | Pnnm (58) | <(2; 5) + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pnnm (58) | <2; 5; 3 + (0, 0, 1)> | a, b, 3c | | | Pnnm (58) | <2; 3 + (0, 0, 3); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pnnm (58) | <2; 3 + (0, 0, 5); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pnnm (58) | <(2; 5) + (2u, 0, 0); 3 + (p/2 - 1/2 + 2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] b' = pb
| Pnnm (58) | <(2; 5) + (0, 2u, 0); 3 + (0, p/2 - 1/2, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| Pnnm (58) | <2; 3 + (0, 0, p/2 - 1/2 + 2u); 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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I Minimal translationengleiche supergroups
| [2] P4/mnc (128); [2] P42/mnm (136) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Amam (63, Cmcm); [2] Bbmm (63, Cmcm); [2] Cccm (66); [2] Immm (71) |
| [2] a' = 1/2a Pncm (53, Pmna); [2] b' = 1/2b Pcnm (53, Pmna); [2] c' = 1/2c Pbam (55) |
