UNIQUE AXIS b, CELL CHOICE 1
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 + 1/2, -z + 1/2 | (3) -x, -y, -z | (4) x, -y + 1/2, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] P1c1 (7) | 1; 4 |
| 0, 1/4, 0
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| [2] P1211 (4) | 1; 2 |
| 0, 0, 1/4
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| [2] P-1 (2) | 1; 3 |
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II Maximal klassengleiche subgroups
[2] a' = 2a
| P121/c1 (14) | <2; 3> | 2a, b, c | |
| P121/c1 (14) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| P121/n1 (14, P121/c1) | <3; 2 + (1, 0, 0)> | 2a, b, -2a + c | |
| P121/n1 (14, P121/c1) | <2 + (2, 0, 0); 3 + (1, 0, 0)> | 2a, b, -2a + c | 1/2, 0, 0 |
[3] b' = 3b
 | P121/c1 (14) | <3; 2 + (0, 1, 0)> | a, 3b, c | | | P121/c1 (14) | <2 + (0, 1, 0); 3 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P121/c1 (14) | <2 + (0, 1, 0); 3 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| P121/c1 (14) | <3; 2 + (0, 0, 1)> | a, b, 3c | | | P121/c1 (14) | <2 + (0, 0, 3); 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P121/c1 (14) | <2 + (0, 0, 5); 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| P121/c1 (14) | <2; 3> | 3a, b, c | | | P121/c1 (14) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P121/c1 (14) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] a' = 3a, c' = -2a + c
| P121/c1 (14) | <3; 2 + (-1, 0, 0)> | 3a, b, -2a + c | | | P121/c1 (14) | <2 + (1, 0, 0); 3 + (2, 0, 0)> | 3a, b, -2a + c | 1, 0, 0 | | P121/c1 (14) | <2 + (3, 0, 0); 3 + (4, 0, 0)> | 3a, b, -2a + c | 2, 0, 0 |
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[3] a' = 3a, c' = -4a + c
| P121/c1 (14) | <3; 2 + (-2, 0, 0)> | 3a, b, -4a + c | | | P121/c1 (14) | <2 + (0, 0, 0); 3 + (2, 0, 0)> | 3a, b, -4a + c | 1, 0, 0 | | P121/c1 (14) | <2 + (2, 0, 0); 3 + (4, 0, 0)> | 3a, b, -4a + c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| P121/c1 (14) | <2 + (0, p/2 - 1/2, 0); 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] c' = pc
| P121/c1 (14) | <2 + (0, 0, p/2 - 1/2 + 2u); 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, c' = -2qa + c
| P121/c1 (14) | <2 + (-q + 2u, 0, 0); 3 + (2u, 0, 0)> | pa, b, -2qa + 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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I Minimal translationengleiche supergroups
| [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pbcn (60); [2] Pbca (61); [2] Pnma (62); [2] Cmce (64) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A12/m1 (12, C12/m1); [2] C12/c1 (15); [2] I12/c1 (15, C12/c1) |
| [2] c' = 1/2c P121/m1 (11); [2] 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); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x + 1/2, -y, z + 1/2 | (3) -x, -y, -z | (4) x + 1/2, y, -z + 1/2 |
|
I Maximal translationengleiche subgroups
| [2] P11a (7) | 1; 4 |
| 0, 0, 1/4
|
| [2] P1121 (4) | 1; 2 |
| 1/4, 0, 0
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| [2] P-1 (2) | 1; 3 |
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II Maximal klassengleiche subgroups
[2] b' = 2b
| P1121/a (14) | <2; 3> | a, 2b, c | |
| P1121/a (14) | <(2; 3) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
| P1121/n (14, P1121/a) | <3; 2 + (0, 1, 0)> | a - 2b, 2b, c | |
| P1121/n (14, P1121/a) | <2 + (0, 2, 0); 3 + (0, 1, 0)> | a - 2b, 2b, c | 0, 1/2, 0 |
[3] c' = 3c
| P1121/a (14) | <3; 2 + (0, 0, 1)> | a, b, 3c | | | P1121/a (14) | <2 + (0, 0, 1); 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P1121/a (14) | <2 + (0, 0, 1); 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| P1121/a (14) | <3; 2 + (1, 0, 0)> | 3a, b, c | | | P1121/a (14) | <2 + (3, 0, 0); 3 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P1121/a (14) | <2 + (5, 0, 0); 3 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| P1121/a (14) | <2; 3> | a, 3b, c | | | P1121/a (14) | <(2; 3) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P1121/a (14) | <(2; 3) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] a' = a - 2b, b' = 3b
| P1121/a (14) | <3; 2 + (0, -1, 0)> | a - 2b, 3b, c | | | P1121/a (14) | <2 + (0, 1, 0); 3 + (0, 2, 0)> | a - 2b, 3b, c | 0, 1, 0 | | P1121/a (14) | <2 + (0, 3, 0); 3 + (0, 4, 0)> | a - 2b, 3b, c | 0, 2, 0 |
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[3] a' = a - 4b, b' = 3b
| P1121/a (14) | <3; 2 + (0, -2, 0)> | a - 4b, 3b, c | | | P1121/a (14) | <2 + (0, 0, 0); 3 + (0, 2, 0)> | a - 4b, 3b, c | 0, 1, 0 | | P1121/a (14) | <2 + (0, 2, 0); 3 + (0, 4, 0)> | a - 4b, 3b, c | 0, 2, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P1121/a (14) | <2 + (0, 0, p/2 - 1/2); 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
| P1121/a (14) | <2 + (p/2 - 1/2 + 2u, 0, 0); 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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[p] a' = a - 2qb, b' = pb
| P1121/a (14) | <2 + (0, -q + 2u, 0); 3 + (0, 2u, 0)> | a - 2qb, pb, c | 0, u, 0 | | | p > 2; 0 ≤ q < p; 0 ≤ u < p
p conjugate subgroups for each pair of q and prime p |
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I Minimal translationengleiche supergroups
| [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pbcn (60); [2] Pbca (61); [2] Pnma (62); [2] Cmce (64) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A112/a (15); [2] B112/m (12, A112/m); [2] I112/a (15, A112/a) |
| [2] a' = 1/2a P1121/m (11); [2] c' = 1/2c P112/a (13) |
