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)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 0)+ |
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I Maximal translationengleiche subgroups
| [2] C1 (1, P1) | 1+ | 1/2(a - b), 1/2(a + b), c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P1a1 (7, P1c1) | 1; 2 + (1/2, 1/2, 0) | -a - c, b, a | 0, 1/4, 0 |
| [2] P1m1 (6) | 1; 2 | | |
[2] c' = 2c
| C1c1 (9) | <2 + (0, 0, 1)> | a, b, 2c | |
| I1c1 (9, C1c1) | <2 + (0, 0, 1)> | a - 2c, b, 2c | |
| C1m1 (8) | <2> | a, b, 2c | |
| I1m1 (8, C1m1) | <2> | a - 2c, b, 2c | |
[3] b' = 3b
 | C1m1 (8) | <2> | a, 3b, c | | | C1m1 (8) | <2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | C1m1 (8) | <2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
[3] a' = a - 2c, c' = 3c
[3] a' = a - 4c, c' = 3c
[3] a' = 3a
- Series of maximal isomorphic subgroups
[p] b' = pb
| C1m1 (8) | <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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[p] a' = a - 2qc, c' = pc
| C1m1 (8) | <2> | a - 2qc, b, pc | | | | p > 1; 0 ≤ q < p
no conjugate subgroups |
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[p] a' = pa
| C1m1 (8) | <2> | pa, b, c | | | | p > 2
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] C12/m1 (12); [2] Cmm2 (35); [2] Cmc21 (36); [2] Amm2 (38); [2] Aem2 (39); [2] Fmm2 (42); [2] Imm2 (44); [2] Ima2 (46); [3] P3m1 (156); [3] P31m (157); [3] R3m (160) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b P1m1 (6) |
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)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (0, 1/2, 1/2)+ |
| |
I Maximal translationengleiche subgroups
| [2] A1 (1, P1) | 1+ | a, 1/2(b - c), 1/2(b + c)
|
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P11b (7, P11a) | 1; 2 + (0, 1/2, 1/2) | b, -a - b, c | 0, 0, 1/4 |
| [2] P11m (6) | 1; 2 | | |
[2] a' = 2a
| A11a (9) | <2 + (1, 0, 0)> | 2a, b, c | |
| I11a (9, A11a) | <2 + (1, 0, 0)> | 2a, -2a + b, c | |
| A11m (8) | <2> | 2a, b, c | |
| I11m (8, A11m) | <2> | 2a, -2a + b, c | |
[3] c' = 3c
| A11m (8) | <2> | a, b, 3c | | | A11m (8) | <2 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | A11m (8) | <2 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = 3a
[3] a' = 3a, b' = -2a + b
| A11m (8) | <2> | 3a, -2a + b, c | |
[3] a' = 3a, b' = -4a + b
| A11m (8) | <2> | 3a, -4a + b, c | |
[3] b' = 3b
- Series of maximal isomorphic subgroups
[p] c' = pc
| A11m (8) | <2 + (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
| A11m (8) | <2> | pa, -2qa + b, c | | | | p > 1; 0 ≤ q < p
no conjugate subgroups |
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[p] b' = pb
| A11m (8) | <2> | a, pb, c | | | | p > 2
no conjugate subgroups |
|
I Minimal translationengleiche supergroups
| [2] A112/m (12); [2] Cmm2 (35); [2] Cmc21 (36); [2] Amm2 (38); [2] Aem2 (39); [2] Fmm2 (42); [2] Imm2 (44); [2] Ima2 (46); [3] P3m1 (156); [3] P31m (157); [3] R3m (160) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] b' = 1/2b, c' = 1/2c P11m (6) |
