Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y, z + 1/2 | (3) -x, y + 1/2, -z + 1/2 | (4) x + 1/2, -y + 1/2, -z |
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I Maximal translationengleiche subgroups
| [2] I1121 (5, A112) | (1; 2)+ | b, -a - b, c
| 0, 1/4, 0
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| [2] I1211 (5, C121) | (1; 3)+ | -a - c, b, a
| 1/4, 0, 0
|
| [2] I2111 (5, C121) | (1; 4)+ | -b - c, a, c
| 0, 0, 1/4
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P212121 (19) | 1; 2; 3; 4 | | |
| [2] P2221 (17) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | | 1/4, 0, 1/4 |
| [2] P2212 (17, P2221) | 1; 3; (2; 4) + (1/2, 1/2, 1/2) | c, a, b | 0, 1/4, 1/4 |
| [2] P2122 (17, P2221) | 1; 4; (2; 3) + (1/2, 1/2, 1/2) | b, c, a | 1/4, 1/4, 0 |
[3] a' = 3a
 | I212121 (24) | <3; 2 + (1, 0, 0)> | 3a, b, c | | | I212121 (24) | <2 + (3, 0, 0); 3 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | I212121 (24) | <2 + (5, 0, 0); 3 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| I212121 (24) | <2; 3 + (0, 1, 0)> | a, 3b, c | | | I212121 (24) | <2 + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | I212121 (24) | <2 + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| I212121 (24) | <(2; 3) + (0, 0, 1)> | a, b, 3c | | | I212121 (24) | <2 + (0, 0, 1); 3 + (0, 0, 3)> | a, b, 3c | 0, 0, 1 | | I212121 (24) | <2 + (0, 0, 1); 3 + (0, 0, 5)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| I212121 (24) | <2 + (p/2 - 1/2 + 2u, 0, 0); 3 + (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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[p] b' = pb
| I212121 (24) | <2 + (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 |
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[p] c' = pc
| I212121 (24) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/2 - 1/2 + 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] Ibca (73); [2] Imma (74); [2] I4122 (98); [2] I-42d (122); [3] I213 (199) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a A222 (21, C222); [2] b' = 1/2b B222 (21, C222); [2] c' = 1/2c C222 (21) |
