UNIQUE AXIS b
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] b' = 2b
| P1211 (4) | <2 + (0, 1, 0)> | a, 2b, c | |
| P121 (3) | <2> | a, 2b, c | |
[2] c' = 2c
| P121 (3) | <2> | a, b, 2c | |
| P121 (3) | <2 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] a' = 2a
| P121 (3) | <2> | 2a, b, c | |
| P121 (3) | <2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] a' = 2a, c' = 2c
| B121 (3, P121) | <2> | a - c, b, 2c | |
| B121 (3, P121) | <2 + (0, 0, 1)> | a - c, b, 2c | 0, 0, 1/2 |
[2] a' = 2a, b' = 2b
| C121 (5) | <2> | 2a, 2b, c | |
| C121 (5) | <2 + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
[2] b' = 2b, c' = 2c
| A121 (5, C121) | <2> | 2c, 2b, -a - 2c | |
| A121 (5, C121) | <2 + (0, 0, 1)> | 2c, 2b, -a - 2c | 0, 0, 1/2 |
[2] a' = 2a, b' = 2b, c' = 2c
| F121 (5, C121) | <2> | 2a, 2b, -a + c | |
| F121 (5, C121) | <2 + (1, 0, 0)> | 2a, 2b, -a + c | 1/2, 0, 0 |
[3] b' = 3b
[3] c' = 3c
 | P121 (3) | <2> | a, b, 3c | | | P121 (3) | <2 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P121 (3) | <2 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = a - c, c' = 3c
| P121 (3) | <2> | a - c, b, 3c | | | P121 (3) | <2 + (0, 0, 2)> | a - c, b, 3c | 0, 0, 1 | | P121 (3) | <2 + (0, 0, 4)> | a - c, b, 3c | 0, 0, 2 |
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[3] a' = a - 2c, c' = 3c
| P121 (3) | <2> | a - 2c, b, 3c | | | P121 (3) | <2 + (0, 0, 2)> | a - 2c, b, 3c | 0, 0, 1 | | P121 (3) | <2 + (0, 0, 4)> | a - 2c, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| P121 (3) | <2> | 3a, b, c | | | P121 (3) | <2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P121 (3) | <2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| P121 (3) | <2> | a, pb, c | | | | p > 1
no conjugate subgroups |
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[p] a' = a - qc, c' = pc
| P121 (3) | <2 + (0, 0, 2u)> | a - qc, b, pc | 0, 0, u | | | p > 2; 0 ≤ q < p; 0 ≤ u < p
p conjugate subgroups for each pair of q and prime p |
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[p] a' = pa
| P121 (3) | <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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I Minimal translationengleiche supergroups
| [2] P12/m1 (10); [2] P12/c1 (13); [2] P222 (16); [2] P2221 (17); [2] P21212 (18); [2] C222 (21); [2] Pmm2 (25); [2] Pcc2 (27); [2] Pma2 (28); [2] Pnc2 (30); [2] Pba2 (32); [2] Pnn2 (34); [2] Cmm2 (35); [2] Ccc2 (37); [2] P4 (75); [2] P42 (77); [2] P-4 (81); [3] P6 (168); [3] P62 (171); [3] P64 (172) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C121 (5); [2] A121 (5, C121); [2] I121 (5, C121) |
UNIQUE AXIS c
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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I Maximal translationengleiche subgroups
II Maximal klassengleiche subgroups
[2] c' = 2c
| P1121 (4) | <2 + (0, 0, 1)> | a, b, 2c | |
| P112 (3) | <2> | a, b, 2c | |
[2] a' = 2a
| P112 (3) | <2> | 2a, b, c | |
| P112 (3) | <2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| P112 (3) | <2> | a, 2b, c | |
| P112 (3) | <2 + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] a' = 2a, b' = 2b
| C112 (3, P112) | <2> | 2a, -a + b, c | |
| C112 (3, P112) | <2 + (1, 0, 0)> | 2a, -a + b, c | 1/2, 0, 0 |
[2] b' = 2b, c' = 2c
| A112 (5) | <2> | a, 2b, 2c | |
| A112 (5) | <2 + (0, 1, 0)> | a, 2b, 2c | 0, 1/2, 0 |
[2] a' = 2a, c' = 2c
| B112 (5, A112) | <2> | -2a - b, 2a, 2c | |
| B112 (5, A112) | <2 + (1, 0, 0)> | -2a - b, 2a, 2c | 1/2, 0, 0 |
[2] a' = 2a, b' = 2b, c' = 2c
| F112 (5, A112) | <2> | a - b, 2b, 2c | |
| F112 (5, A112) | <2 + (0, 1, 0)> | a - b, 2b, 2c | 0, 1/2, 0 |
[3] c' = 3c
[3] a' = 3a
| P112 (3) | <2> | 3a, b, c | | | P112 (3) | <2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P112 (3) | <2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -a + b
| P112 (3) | <2> | 3a, -a + b, c | | | P112 (3) | <2 + (2, 0, 0)> | 3a, -a + b, c | 1, 0, 0 | | P112 (3) | <2 + (4, 0, 0)> | 3a, -a + b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -2a + b
| P112 (3) | <2> | 3a, -2a + b, c | | | P112 (3) | <2 + (2, 0, 0)> | 3a, -2a + b, c | 1, 0, 0 | | P112 (3) | <2 + (4, 0, 0)> | 3a, -2a + b, c | 2, 0, 0 |
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[3] b' = 3b
| P112 (3) | <2> | a, 3b, c | | | P112 (3) | <2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P112 (3) | <2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P112 (3) | <2> | a, b, pc | | | | p > 1
no conjugate subgroups |
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[p] a' = pa, b' = -qa + b
| P112 (3) | <2 + (2u, 0, 0)> | pa, -qa + b, c | u, 0, 0 | | | p > 2; 0 ≤ q < p; 0 ≤ u < p
p conjugate subgroups for each pair of q and prime p |
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[p] b' = pb
| P112 (3) | <2 + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P112/m (10); [2] P112/a (13); [2] P222 (16); [2] P2221 (17); [2] P21212 (18); [2] C222 (21); [2] Pmm2 (25); [2] Pcc2 (27); [2] Pma2 (28); [2] Pnc2 (30); [2] Pba2 (32); [2] Pnn2 (34); [2] Cmm2 (35); [2] Ccc2 (37); [2] P4 (75); [2] P42 (77); [2] P-4 (81); [3] P6 (168); [3] P62 (171); [3] P64 (172) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A112 (5); [2] B112 (5, A112); [2] I112 (5, A112) |
