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) -y, x, z + 1/2 | (4) y, -x, z + 1/2 | | (5) -x, -y, -z | (6) x, y, -z | (7) y, -x, -z + 1/2 | (8) -y, x, -z + 1/2 |
|
I Maximal translationengleiche subgroups
| [2] P-4 (81) | 1; 2; 7; 8 |
| 0, 0, 1/4
|
| [2] P42 (77) | 1; 2; 3; 4 |
|
|
| [2] P2/m (10, P112/m) | 1; 2; 5; 6 |
|
|
II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b
| C42/e (86, P42/n) | <2; 3; 5 + (0, 1, 0)> | a - b, a + b, c | 0, 1/2, 0 |
| C42/e (86, P42/n) | <2 + (1, 1, 0); (3; 5) + (1, 0, 0)> | a - b, a + b, c | 1/2, 0, 0 |
| C42/m (84, P42/m) | <2; 3; 5> | a - b, a + b, c | |
| C42/m (84, P42/m) | <(2; 5) + (1, 1, 0); 3 + (1, 0, 0)> | a - b, a + b, c | 1/2, 1/2, 0 |
[3] c' = 3c
 | P42/m (84) | <2; 5; 3 + (0, 0, 1)> | a, b, 3c | | | P42/m (84) | <2; 3 + (0, 0, 1); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P42/m (84) | <2; 3 + (0, 0, 1); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
|
- Series of maximal isomorphic subgroups
[p] c' = pc
| P42/m (84) | <2; 3 + (0, 0, p/2 - 1/2); 5 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p2] a' = pa, b' = pb
| P42/m (84) | <(2; 5) + (2u, 2v, 0); 3 + (u + v, -u + v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 3 (mod 4) |
|
[p = q2 + r2] a' = qa - rb, b' = ra + qb
| P42/m (84) | <(2; 5) + (u, u, 0); 3 + (u, 0, 0)> | qa - rb, ra + qb, c | u, 0, 0 | | | q > 0; r > 0; p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
|
I Minimal translationengleiche supergroups
| [2] P42/mmc (131); [2] P42/mcm (132); [2] P42/mbc (135); [2] P42/mnm (136) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
