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)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (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, z | (3) -x, y, -z | (4) x, -y, -z |
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I Maximal translationengleiche subgroups
| [2] F112 (5, A112) | (1; 2)+ | 1/2(a - b), b, c
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| [2] F121 (5, C121) | (1; 3)+ | a, b, 1/2(-a + c)
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| [2] F211 (5, C121) | (1; 4)+ | c, a, 1/2(b - c)
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] A222 (21, C222) | 1; 2; 3; 4; (1; 2; 3; 4) + (0, 1/2, 1/2) | b, c, a | |
| [2] A222 (21, C222) | 1; 4; (1; 4) + (0, 1/2, 1/2); (2; 3) + (1/2, 0, 1/2); (2; 3) + (1/2, 1/2, 0) | b, c, a | 1/4, 1/4, 1/4 |
| [2] B222 (21, C222) | 1; 2; 3; 4; (1; 2; 3; 4) + (1/2, 0, 1/2) | c, a, b | |
| [2] B222 (21, C222) | 1; 3; (1; 3) + (1/2, 0, 1/2); (2; 4) + (1/2, 1/2, 0); (2; 4) + (0, 1/2, 1/2) | c, a, b | 1/4, 1/4, 1/4 |
| [2] C222 (21) | 1; 2; 3; 4; (1; 2; 3; 4) + (1/2, 1/2, 0) | | |
| [2] C222 (21) | 1; 2; (1; 2) + (1/2, 1/2, 0); (3; 4) + (0, 1/2, 1/2); (3; 4) + (1/2, 0, 1/2) | | 1/4, 1/4, 1/4 |
| [2] A2122 (20, C2221) | 1; 2; (1; 2) + (0, 1/2, 1/2); (3; 4) + (1/2, 0, 1/2); (3; 4) + (1/2, 1/2, 0) | b, c, a | 1/4, 0, 1/4 |
| [2] A2122 (20, C2221) | 1; 3; (1; 3) + (0, 1/2, 1/2); (2; 4) + (1/2, 0, 1/2); (2; 4) + (1/2, 1/2, 0) | b, c, a | 0, 1/4, 0 |
| [2] B2212 (20, C2221) | 1; 2; (1; 2) + (1/2, 0, 1/2); (3; 4) + (1/2, 1/2, 0); (3; 4) + (0, 1/2, 1/2) | c, a, b | 0, 0, 1/4 |
| [2] B2212 (20, C2221) | 1; 4; (1; 4) + (1/2, 0, 1/2); (2; 3) + (1/2, 1/2, 0); (2; 3) + (0, 1/2, 1/2) | c, a, b | 1/4, 1/4, 0 |
| [2] C2221 (20) | 1; 3; (1; 3) + (1/2, 1/2, 0); (2; 4) + (0, 1/2, 1/2); (2; 4) + (1/2, 0, 1/2) | | 0, 1/4, 1/4 |
| [2] C2221 (20) | 1; 4; (1; 4) + (1/2, 1/2, 0); (2; 3) + (0, 1/2, 1/2); (2; 3) + (1/2, 0, 1/2) | | 1/4, 0, 0 |
[3] a' = 3a
 | F222 (22) | <2; 3> | 3a, b, c | | | F222 (22) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | F222 (22) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| F222 (22) | <2; 3> | a, 3b, c | | | F222 (22) | <3; 2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | F222 (22) | <3; 2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| F222 (22) | <2; 3> | a, b, 3c | | | F222 (22) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | F222 (22) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| F222 (22) | <(2; 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
| F222 (22) | <3; 2 + (0, 2u, 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
| F222 (22) | <2; 3 + (0, 0, 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] Fmmm (69); [2] Fddd (70); [2] I422 (97); [2] I4122 (98); [2] I-4m2 (119); [2] I-4c2 (120); [3] F23 (196) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c P222 (16) |
