Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); t(1/2, 0, 1/2); (2); (3); (5); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (0, 1/2, 1/2)+ (1/2, 0, 1/2)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x, -y + 1/2, z + 1/2 | (3) -x + 1/2, y + 1/2, -z | (4) x + 1/2, -y, -z + 1/2 | | (5) z, x, y | (6) z + 1/2, -x, -y + 1/2 | (7) -z, -x + 1/2, y + 1/2 | (8) -z + 1/2, x + 1/2, -y | | (9) y, z, x | (10) -y + 1/2, z + 1/2, -x | (11) y + 1/2, -z, -x + 1/2 | (12) -y, -z + 1/2, x + 1/2 | | (13) y + 3/4, x + 1/4, -z + 3/4 | (14) -y + 1/4, -x + 1/4, -z + 1/4 | (15) y + 1/4, -x + 3/4, z + 3/4 | (16) -y + 3/4, x + 3/4, z + 1/4 | | (17) x + 3/4, z + 1/4, -y + 3/4 | (18) -x + 3/4, z + 3/4, y + 1/4 | (19) -x + 1/4, -z + 1/4, -y + 1/4 | (20) x + 1/4, -z + 3/4, y + 3/4 | | (21) z + 3/4, y + 1/4, -x + 3/4 | (22) z + 1/4, -y + 3/4, x + 3/4 | (23) -z + 3/4, y + 3/4, x + 1/4 | (24) -z + 1/4, -y + 1/4, -x + 1/4 |
|
I Maximal translationengleiche subgroups
| [2] F231 (196, F23) | (1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12)+ |
|
|
 | [3] F4112 (98, I4122) | (1; 2; 3; 4; 13; 14; 15; 16)+ | 1/2(a - b), 1/2(a + b), c
|
| | [3] F4112 (98, I4122) | (1; 4; 2; 3; 18; 19; 17; 20)+ | 1/2(b - c), 1/2(b + c), a
|
| | [3] F4112 (98, I4122) | (1; 3; 4; 2; 22; 24; 23; 21)+ | 1/2(-a + c), 1/2(a + c), b
|
|
|
 | [4] F132 (155, R32) | (1; 5; 9; 14; 19; 24)+ | 1/2(-a + b), 1/2(-b + c), a + b + c
| 1/8, 1/8, 1/8
| | [4] F132 (155, R32) | (1; 6; 12; 13; 18; 24)+ | 1/2(a + b), 1/2(-b - c), -a + b - c
| 3/8, 1/8, 3/8
| | [4] F132 (155, R32) | (1; 7; 10; 13; 19; 22)+ | 1/2(-a - b), 1/2(b - c), a - b - c
| 1/8, 3/8, 3/8
| | [4] F132 (155, R32) | (1; 8; 11; 14; 18; 22)+ | 1/2(a - b), 1/2(b + c), -a - b + c
| 3/8, 3/8, 1/8
|
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [4] P4132 (213) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24 | | 1/4, 1/4, 1/4 | | [4] P4132 (213) | 1; 2; 3; 4; 13; 14; 15; 16; (5; 6; 7; 8; 21; 22; 23; 24) + (1/2, 0, 1/2); (9; 10; 11; 12; 17; 18; 19; 20) + (0, 1/2, 1/2) | | 3/4, 3/4, 1/4 | | [4] P4132 (213) | 1; 2; 3; 4; 17; 18; 19; 20; (5; 6; 7; 8; 13; 14; 15; 16) + (1/2, 1/2, 0); (9; 10; 11; 12; 21; 22; 23; 24) + (1/2, 0, 1/2) | | 1/4, 3/4, 3/4 | | [4] P4132 (213) | 1; 2; 3; 4; 21; 22; 23; 24; (5; 6; 7; 8; 17; 18; 19; 20) + (0, 1/2, 1/2); (9; 10; 11; 12; 13; 14; 15; 16) + (1/2, 1/2, 0) | | 3/4, 1/4, 3/4 |
|
| [4] P4332 (212) | 1; 5; 9; 14; 19; 24; (2; 7; 12; 13; 17; 21) + (1/2, 1/2, 0); (3; 8; 10; 15; 20; 22) + (1/2, 0, 1/2); (4; 6; 11; 16; 18; 23) + (0, 1/2, 1/2) | | | | [4] P4332 (212) | 1; 6; 12; 13; 18; 24; (2; 8; 9; 14; 20; 21) + (1/2, 1/2, 0); (3; 7; 11; 16; 17; 22) + (1/2, 0, 1/2); (4; 5; 10; 15; 19; 23) + (0, 1/2, 1/2) | | 1/2, 0, 1/2 | | [4] P4332 (212) | 1; 7; 10; 13; 19; 22; (2; 5; 11; 14; 17; 23) + (1/2, 1/2, 0); (3; 6; 9; 16; 20; 24) + (1/2, 0, 1/2); (4; 8; 12; 15; 18; 21) + (0, 1/2, 1/2) | | 0, 1/2, 1/2 | | [4] P4332 (212) | 1; 8; 11; 14; 18; 22; (2; 6; 10; 13; 20; 23) + (1/2, 1/2, 0); (3; 5; 12; 15; 17; 24) + (1/2, 0, 1/2); (4; 7; 9; 16; 19; 21) + (0, 1/2, 1/2) | | 1/2, 1/2, 0 |
|
- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| F4132 (210) | <2 + (1/2 + 2u, p/2 + 2v, p/2 - 1/2); 3 + (p/2 + 2u, p/2 - 1/2, 1/2 + 2w); 5 + (u - w, -u + v, -v + w); 13 + (3p/4 - 3/4 + u - v, p/4 - 1/4 - u + v, 3p/4 - 1/4 + 2w)> | pa, pb, pc | 1/4 + u, 1/4 + v, 1/4 + w | | | p > 2; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for prime p ≡ 3 (mod 4) |
| F4132 (210) | <2 + (2u, p/2 - 1/2 + 2v, p/2 - 1/2); 3 + (p/2 - 1/2 + 2u, p/2 - 1/2, 2w); 5 + (u - w, -u + v, -v + w); 13 + (3p/4 - 3/4 + u - v, p/4 - 1/4 - u + v, 3p/4 - 3/4 + 2w)> | pa, pb, pc | u, v, w | | | p > 4; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for prime p ≡ 1 (mod 4) |
|
I Minimal translationengleiche supergroups
| [2] Fd-3m (227); [2] Fd-3c (228) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c P4232 (208) |
