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 + 1/4, -y + 1/4, z + 1/4 | (4) -x + 1/4, y + 1/4, z + 1/4 |
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I Maximal translationengleiche subgroups
| [2] F1d1 (9, C1c1) | (1; 3)+ | -c, b, 1/2(a + c)
| 0, 1/8, 0
|
| [2] Fd11 (9, C1c1) | (1; 4)+ | -b, a, 1/2(b + c)
| 1/8, 0, 0
|
| [2] F112 (5, A112) | (1; 2)+ | 1/2(a - b), b, c
|
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II Maximal klassengleiche subgroups
- Loss of centring translations
[3] a' = 3a
 | Fdd2 (43) | <(2; 3) + (1/2, 1/2, 0)> | 3a, b, c | 1/4, 1/4, 0 | | Fdd2 (43) | <2 + (5/2, 1/2, 0); 3 + (1/2, 1/2, 0)> | 3a, b, c | 5/4, 1/4, 0 | | Fdd2 (43) | <2 + (9/2, 1/2, 0); 3 + (1/2, 1/2, 0)> | 3a, b, c | 9/4, 1/4, 0 |
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[3] b' = 3b
| Fdd2 (43) | <2 + (1/2, 1/2, 0); 3 + (0, 1, 0)> | a, 3b, c | 1/4, 1/4, 0 | | Fdd2 (43) | <2 + (1/2, 5/2, 0); 3 + (0, 3, 0)> | a, 3b, c | 1/4, 5/4, 0 | | Fdd2 (43) | <2 + (1/2, 9/2, 0); 3 + (0, 5, 0)> | a, 3b, c | 1/4, 9/4, 0 |
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[3] c' = 3c
| Fdd2 (43) | <2 + (1/2, 1/2, 0); 3 + (0, 1/2, 1/2)> | a, b, 3c | 1/4, 1/4, 0 |
- Series of maximal isomorphic subgroups
[p] a' = pa
| Fdd2 (43) | <2 + (1/2 + 2u, 1/2, 0); 3 + (p/4 - 1/4, 1/2, 0)> | pa, b, c | 1/4 + u, 1/4, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fdd2 (43) | <2 + (2u, 0, 0); 3 + (p/4 - 1/4, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
|
[p] b' = pb
| Fdd2 (43) | <2 + (1/2, 1/2 + 2u, 0); 3 + (0, p/4 + 1/4 + 2u, 0)> | a, pb, c | 1/4, 1/4 + u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fdd2 (43) | <2 + (0, 2u, 0); 3 + (0, p/4 - 1/4 + 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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[p] c' = pc
| Fdd2 (43) | <2 + (1/2, 1/2, 0); 3 + (0, 1/2, p/4 - 1/4)> | a, b, pc | 1/4, 1/4, 0 | | | p > 2; p ≡ 3 (mod 4)
no conjugate subgroups |
| Fdd2 (43) | <2; 3 + (0, 0, p/4 - 1/4)> | a, b, pc | | | | p > 4; p ≡ 1 (mod 4)
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] Fddd (70); [2] I41md (109); [2] I41cd (110); [2] I-42d (122) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c Pnn2 (34) |
