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] P1211 (4) | 1; 2 + (1/2, 1/2, 0) | | 1/4, 0, 0 |
| [2] P121 (3) | 1; 2 | | |
[2] c' = 2c
| C121 (5) | <2> | a, b, 2c | |
| C121 (5) | <2 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| I121 (5, C121) | <2> | a - 2c, b, 2c | |
| I121 (5, C121) | <2 + (0, 0, 1)> | a - 2c, b, 2c | 0, 0, 1/2 |
[3] b' = 3b
[3] c' = 3c
 | C121 (5) | <2> | a, b, 3c | | | C121 (5) | <2 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | C121 (5) | <2 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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[3] a' = a - 2c, c' = 3c
| C121 (5) | <2> | a - 2c, b, 3c | | | C121 (5) | <2 + (0, 0, 2)> | a - 2c, b, 3c | 0, 0, 1 | | C121 (5) | <2 + (0, 0, 4)> | a - 2c, b, 3c | 0, 0, 2 |
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[3] a' = a - 4c, c' = 3c
| C121 (5) | <2> | a - 4c, b, 3c | | | C121 (5) | <2 + (0, 0, 2)> | a - 4c, b, 3c | 0, 0, 1 | | C121 (5) | <2 + (0, 0, 4)> | a - 4c, b, 3c | 0, 0, 2 |
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[3] a' = 3a
| C121 (5) | <2> | 3a, b, c | | | C121 (5) | <2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | C121 (5) | <2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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- Series of maximal isomorphic subgroups
[p] b' = pb
| C121 (5) | <2> | a, pb, c | | | | p > 2
no conjugate subgroups |
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[p] a' = a - 2qc, c' = pc
| C121 (5) | <2 + (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
| C121 (5) | <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] C12/m1 (12); [2] C12/c1 (15); [2] C2221 (20); [2] C222 (21); [2] F222 (22); [2] I222 (23); [2] I212121 (24); [2] Amm2 (38); [2] Aem2 (39); [2] Ama2 (40); [2] Aea2 (41); [2] Fmm2 (42); [2] Fdd2 (43); [2] Imm2 (44); [2] Iba2 (45); [2] Ima2 (46); [2] I4 (79); [2] I41 (80); [2] I-4 (82); [3] P312 (149); [3] P321 (150); [3] P3112 (151); [3] P3121 (152); [3] P3212 (153); [3] P3221 (154); [3] R32 (155) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b P121 (3) |
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] P1121 (4) | 1; 2 + (0, 1/2, 1/2) | | 0, 1/4, 0 |
| [2] P112 (3) | 1; 2 | | |
[2] a' = 2a
| A112 (5) | <2> | 2a, b, c | |
| A112 (5) | <2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| I112 (5, A112) | <2> | 2a, -2a + b, c | |
| I112 (5, A112) | <2 + (1, 0, 0)> | 2a, -2a + b, c | 1/2, 0, 0 |
[3] c' = 3c
[3] a' = 3a
| A112 (5) | <2> | 3a, b, c | | | A112 (5) | <2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | A112 (5) | <2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -2a + b
| A112 (5) | <2> | 3a, -2a + b, c | | | A112 (5) | <2 + (2, 0, 0)> | 3a, -2a + b, c | 1, 0, 0 | | A112 (5) | <2 + (4, 0, 0)> | 3a, -2a + b, c | 2, 0, 0 |
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[3] a' = 3a, b' = -4a + b
| A112 (5) | <2> | 3a, -4a + b, c | | | A112 (5) | <2 + (2, 0, 0)> | 3a, -4a + b, c | 1, 0, 0 | | A112 (5) | <2 + (4, 0, 0)> | 3a, -4a + b, c | 2, 0, 0 |
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[3] b' = 3b
| A112 (5) | <2> | a, 3b, c | | | A112 (5) | <2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | A112 (5) | <2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| A112 (5) | <2> | a, b, pc | | | | p > 2
no conjugate subgroups |
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[p] a' = pa, b' = -2qa + b
| A112 (5) | <2 + (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 (5) | <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] A112/m (12); [2] A112/a (15); [2] C2221 (20); [2] C222 (21); [2] F222 (22); [2] I222 (23); [2] I212121 (24); [2] Amm2 (38); [2] Aem2 (39); [2] Ama2 (40); [2] Aea2 (41); [2] Fmm2 (42); [2] Fdd2 (43); [2] Imm2 (44); [2] Iba2 (45); [2] Ima2 (46); [2] I4 (79); [2] I41 (80); [2] I-4 (82); [3] P312 (149); [3] P321 (150); [3] P3112 (151); [3] P3121 (152); [3] P3212 (153); [3] P3221 (154); [3] R32 (155) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] b' = 1/2b, c' = 1/2c P112 (3) |
