Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x, -y, z | (3) -x + 1/2, y + 1/2, -z | (4) x + 1/2, -y + 1/2, -z | | (5) -x, -y, -z | (6) x, y, -z | (7) x + 1/2, -y + 1/2, z | (8) -x + 1/2, y + 1/2, z |
|
I Maximal translationengleiche subgroups
| [2] Pba2 (32) | 1; 2; 7; 8 |
|
|
| [2] Pb21m (26, Pmc21) | 1; 3; 6; 8 | c, a, b
| 1/4, 0, 0
|
| [2] P21am (26, Pmc21) | 1; 4; 6; 7 | c, b, -a
| 0, 1/4, 0
|
| [2] P21212 (18) | 1; 2; 3; 4 |
|
|
| [2] P121/a1 (14, P121/c1) | 1; 3; 5; 7 | -a - c, b, a
|
|
| [2] P21/b11 (14, P121/c1) | 1; 4; 5; 8 | c, a, b
|
|
| [2] P112/m (10) | 1; 2; 5; 6 |
|
|
II Maximal klassengleiche subgroups
[2] c' = 2c
| Pnam (62, Pnma) | <3; 5; 2 + (0, 0, 1)> | a, -2c, b | |
| Pnam (62, Pnma) | <(2; 3; 5) + (0, 0, 1)> | a, -2c, b | 0, 0, 1/2 |
| Pbnm (62, Pnma) | <5; (2; 3) + (0, 0, 1)> | b, 2c, a | |
| Pbnm (62, Pnma) | <3; (2; 5) + (0, 0, 1)> | b, 2c, a | 0, 0, 1/2 |
| Pnnm (58) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Pnnm (58) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pbam (55) | <2; 3; 5> | a, b, 2c | |
| Pbam (55) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a
 | Pbam (55) | <2; 5; 3 + (1, 0, 0)> | 3a, b, c | | | Pbam (55) | <(2; 5) + (2, 0, 0); 3 + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pbam (55) | <(2; 5) + (4, 0, 0); 3 + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
|
[3] b' = 3b
| Pbam (55) | <2; 5; 3 + (0, 1, 0)> | a, 3b, c | | | Pbam (55) | <(2; 5) + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | Pbam (55) | <(2; 5) + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
|
[3] c' = 3c
| Pbam (55) | <2; 3; 5> | a, b, 3c | | | Pbam (55) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pbam (55) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
|
- Series of maximal isomorphic subgroups
[p] a' = pa
| Pbam (55) | <(2; 5) + (2u, 0, 0); 3 + (p/2 - 1/2 + 2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] b' = pb
| Pbam (55) | <(2; 5) + (0, 2u, 0); 3 + (0, p/2 - 1/2, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] c' = pc
| Pbam (55) | <2; (3; 5) + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
I Minimal translationengleiche supergroups
| [2] P4/mbm (127); [2] P42/mbc (135) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Aeam (64, Cmce); [2] Bbem (64, Cmce); [2] Cmmm (65); [2] Ibam (72) |
| [2] a' = 1/2a Pbmm (51, Pmma); [2] b' = 1/2b Pmam (51, Pmma) |
