Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
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 | (4) x + 1/2, -y + 1/2, -z |
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I Maximal translationengleiche subgroups
| [2] P1211 (4) | 1; 3 |
| 1/4, 0, 0
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| [2] P2111 (4, P1211) | 1; 4 | c, a, b
| 0, 1/4, 0
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| [2] P112 (3) | 1; 2 |
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P212121 (19) | <3; 2 + (0, 0, 1)> | a, b, 2c | 1/4, 0, 1/2 |
| P212121 (19) | <(2; 3) + (0, 0, 1)> | a, b, 2c | 1/4, 0, 0 |
| P21212 (18) | <2; 3> | a, b, 2c | |
| P21212 (18) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a
 | P21212 (18) | <2; 3 + (1, 0, 0)> | 3a, b, c | | | P21212 (18) | <2 + (2, 0, 0); 3 + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | P21212 (18) | <2 + (4, 0, 0); 3 + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| P21212 (18) | <2; 3 + (0, 1, 0)> | a, 3b, c | | | P21212 (18) | <2 + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | P21212 (18) | <2 + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| P21212 (18) | <2; 3> | a, b, 3c | | | P21212 (18) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P21212 (18) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| P21212 (18) | <2 + (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
| P21212 (18) | <2 + (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
| P21212 (18) | <2; 3 + (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] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pmmn (59); [2] Pbcn (60); [2] P4212 (90); [2] P42212 (94); [2] P-421m (113); [2] P-421c (114) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A2122 (20, C2221); [2] B2212 (20, C2221); [2] C222 (21); [2] I222 (23) |
| [2] a' = 1/2a P2212 (17, P2221); [2] b' = 1/2b P2122 (17, P2221) |
