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 + 1/2, -y, z | (3) -x, y, -z | (4) x + 1/2, -y, -z | | (5) -x, -y, -z | (6) x + 1/2, y, -z | (7) x, -y, z | (8) -x + 1/2, y, z |
|
I Maximal translationengleiche subgroups
| [2] Pm2a (28, Pma2) | 1; 3; 6; 8 | a, -c, b
|
|
| [2] P21ma (26, Pmc21) | 1; 4; 6; 7 | b, c, a
|
|
| [2] Pmm2 (25) | 1; 2; 7; 8 |
| 1/4, 0, 0
|
| [2] P2122 (17, P2221) | 1; 2; 3; 4 | b, c, a
|
|
| [2] P112/a (13) | 1; 2; 5; 6 |
|
|
| [2] P21/m11 (11, P121/m1) | 1; 4; 5; 8 | c, a, b
|
|
| [2] P12/m1 (10) | 1; 3; 5; 7 |
|
|
II Maximal klassengleiche subgroups
[2] b' = 2b
| Pmmn (59) | <5; (2; 3) + (0, 1, 0)> | a, 2b, c | |
| Pmmn (59) | <2; (3; 5) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
| Pbma (57, Pbcm) | <2; 5; 3 + (0, 1, 0)> | c, a, 2b | |
| Pbma (57, Pbcm) | <(2; 3; 5) + (0, 1, 0)> | c, a, 2b | 0, 1/2, 0 |
| Pbmn (53, Pmna) | <3; 5; 2 + (0, 1, 0)> | 2b, c, a | |
| Pbmn (53, Pmna) | <2; 3; 5 + (0, 1, 0)> | 2b, c, a | 0, 1/2, 0 |
| Pmma (51) | <2; 3; 5> | a, 2b, c | |
| Pmma (51) | <3; (2; 5) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] c' = 2c
| Pmca (57, Pbcm) | <5; (2; 3) + (0, 0, 1)> | b, 2c, a | |
| Pmca (57, Pbcm) | <3; (2; 5) + (0, 0, 1)> | b, 2c, a | 0, 0, 1/2 |
| Pcma (55, Pbam) | <3; 5; 2 + (0, 0, 1)> | 2c, a, b | |
| Pcma (55, Pbam) | <(2; 3; 5) + (0, 0, 1)> | 2c, a, b | 0, 0, 1/2 |
| Pcca (54) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Pcca (54) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pmma (51) | <2; 3; 5> | a, b, 2c | |
| Pmma (51) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] b' = 2b, c' = 2c
| Aema (64, Cmce) | <3; 5; 2 + (0, 0, 1)> | 2b, 2c, a | |
| Aema (64, Cmce) | <(2; 3; 5) + (0, 0, 1)> | 2b, 2c, a | 0, 0, 1/2 |
| Aema (64, Cmce) | <2; 5; 3 + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 1/2 |
| Aema (64, Cmce) | <2; 3; 5 + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 0 |
| Amma (63, Cmcm) | <2; 3; 5> | 2b, 2c, a | |
| Amma (63, Cmcm) | <2; (3; 5) + (0, 0, 1)> | 2b, 2c, a | 0, 0, 1/2 |
| Amma (63, Cmcm) | <5; (2; 3) + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 1/2 |
| Amma (63, Cmcm) | <3; (2; 5) + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 0 |
[3] a' = 3a
 | Pmma (51) | <3; 5; 2 + (1, 0, 0)> | 3a, b, c | | | Pmma (51) | <2 + (3, 0, 0); (3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pmma (51) | <2 + (5, 0, 0); (3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
|
[3] b' = 3b
| Pmma (51) | <2; 3; 5> | a, 3b, c | | | Pmma (51) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Pmma (51) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
|
[3] c' = 3c
| Pmma (51) | <2; 3; 5> | a, b, 3c | | | Pmma (51) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pmma (51) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
|
- Series of maximal isomorphic subgroups
[p] a' = pa
| Pmma (51) | <2 + (p/2 - 1/2 + 2u, 0, 0); (3; 5) + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] b' = pb
| Pmma (51) | <3; (2; 5) + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] c' = pc
| Pmma (51) | <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
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Amma (63, Cmcm); [2] Bmmm (65, Cmmm); [2] Cmme (67); [2] Imma (74) |
