UNIQUE AXIS b, CELL CHOICE 1
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x, y, -z + 1/2 | (3) -x, -y, -z | (4) x, -y, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] C1c1 (9) | (1; 4)+ |
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| [2] C121 (5) | (1; 2)+ |
| 0, 0, 1/4
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| [2] C-1 (2, P-1) | (1; 3)+ | 1/2(a - b), 1/2(a + b), c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P121/n1 (14, P121/c1) | 1; 3; (2; 4) + (1/2, 1/2, 0) | c, b, -a - c | |
| [2] P121/c1 (14) | 1; 4; (2; 3) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] P12/c1 (13) | 1; 2; 3; 4 | | |
| [2] P12/n1 (13, P12/c1) | 1; 2; (3; 4) + (1/2, 1/2, 0) | c, b, -a - c | 1/4, 1/4, 0 |
[3] b' = 3b
 | C12/c1 (15) | <2; 3> | a, 3b, c | | | C12/c1 (15) | <2; 3 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | C12/c1 (15) | <2; 3 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| C12/c1 (15) | <3; 2 + (0, 0, 1)> | a, b, 3c | | | C12/c1 (15) | <2 + (0, 0, 3); 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | C12/c1 (15) | <2 + (0, 0, 5); 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = a - 2c, c' = 3c
| C12/c1 (15) | <3; 2 + (0, 0, 1)> | a - 2c, b, 3c | | | C12/c1 (15) | <2 + (0, 0, 3); 3 + (0, 0, 2)> | a - 2c, b, 3c | 0, 0, 1 | | C12/c1 (15) | <2 + (0, 0, 5); 3 + (0, 0, 4)> | a - 2c, b, 3c | 0, 0, 2 |
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[3] a' = a - 4c, c' = 3c
| C12/c1 (15) | <3; 2 + (0, 0, 1)> | a - 4c, b, 3c | | | C12/c1 (15) | <2 + (0, 0, 3); 3 + (0, 0, 2)> | a - 4c, b, 3c | 0, 0, 1 | | C12/c1 (15) | <2 + (0, 0, 5); 3 + (0, 0, 4)> | a - 4c, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| C12/c1 (15) | <2; 3> | 3a, b, c | | | C12/c1 (15) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | C12/c1 (15) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| C12/c1 (15) | <2; 3 + (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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[p] a' = a - 2qc, c' = pc
| C12/c1 (15) | <2 + (0, 0, p/2 - 1/2 + 2u); 3 + (0, 0, 2u)> | a - 2qc, 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
| C12/c1 (15) | <(2; 3) + (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] Cmcm (63); [2] Cmce (64); [2] Cccm (66); [2] Ccce (68); [2] Fddd (70); [2] Ibam (72); [2] Ibca (73); [2] Imma (74); [2] I41/a (88); [3] P-312/c (163, P-31c); [3] P-32/c1 (165, P-3c1); [3] R-32/c (167, R-3c) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C12/m1 (12); [2] a' = 1/2a, b' = 1/2b P12/c1 (13) |
UNIQUE AXIS c, CELL CHOICE 1
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (0, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y, z | (3) -x, -y, -z | (4) x + 1/2, y, -z |
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I Maximal translationengleiche subgroups
| [2] A11a (9) | (1; 4)+ |
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| [2] A112 (5) | (1; 2)+ |
| 1/4, 0, 0
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| [2] A-1 (2, P-1) | (1; 3)+ | a, 1/2(b - c), 1/2(b + c)
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P1121/n (14, P1121/a) | 1; 3; (2; 4) + (0, 1/2, 1/2) | -a - b, a, c | |
| [2] P1121/a (14) | 1; 4; (2; 3) + (0, 1/2, 1/2) | | 0, 1/4, 1/4 |
| [2] P112/a (13) | 1; 2; 3; 4 | | |
| [2] P112/n (13, P112/a) | 1; 2; (3; 4) + (0, 1/2, 1/2) | -a - b, a, c | 0, 1/4, 1/4 |
[3] c' = 3c
| A112/a (15) | <2; 3> | a, b, 3c | | | A112/a (15) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | A112/a (15) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| A112/a (15) | <3; 2 + (1, 0, 0)> | 3a, b, c | | | A112/a (15) | <2 + (3, 0, 0); 3 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | A112/a (15) | <2 + (5, 0, 0); 3 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -2a + b
| A112/a (15) | <3; 2 + (1, 0, 0)> | 3a, -2a + b, c | | | A112/a (15) | <2 + (3, 0, 0); 3 + (2, 0, 0)> | 3a, -2a + b, c | 1, 0, 0 | | A112/a (15) | <2 + (5, 0, 0); 3 + (4, 0, 0)> | 3a, -2a + b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -4a + b
| A112/a (15) | <3; 2 + (1, 0, 0)> | 3a, -4a + b, c | | | A112/a (15) | <2 + (3, 0, 0); 3 + (2, 0, 0)> | 3a, -4a + b, c | 1, 0, 0 | | A112/a (15) | <2 + (5, 0, 0); 3 + (4, 0, 0)> | 3a, -4a + b, c | 2, 0, 0 |
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[3] b' = 3b
| A112/a (15) | <2; 3> | a, 3b, c | | | A112/a (15) | <(2; 3) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | A112/a (15) | <(2; 3) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| A112/a (15) | <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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[p] a' = pa, b' = -2qa + b
| A112/a (15) | <2 + (p/2 - 1/2 + 2u, 0, 0); 3 + (2u, 0, 0)> | pa, -2qa + 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
| A112/a (15) | <(2; 3) + (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] Cmcm (63); [2] Cmce (64); [2] Cccm (66); [2] Ccce (68); [2] Fddd (70); [2] Ibam (72); [2] Ibca (73); [2] Imma (74); [2] I41/a (88); [3] P-312/c (163, P-31c); [3] P-32/c1 (165, P-3c1); [3] R-32/c (167, R-3c) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a A112/m (12); [2] b' = 1/2b, c' = 1/2c P112/a (13) |
