Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) x + 1/2, -y + 1/2, z + 1/2 | (4) -x + 1/2, y + 1/2, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] P1n1 (7, P1c1) | 1; 3 | c, b, -a - c
| 0, 1/4, 0
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| [2] Pn11 (7, P1c1) | 1; 4 | b, a, -b - c
| 1/4, 0, 0
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| [2] P112 (3) | 1; 2 |
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| Fdd2 (43) | <2; 3> | 2a, 2b, 2c | |
| Fdd2 (43) | <3; 2 + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 0, 0 |
| Fdd2 (43) | <(2; 3) + (0, 1, 0)> | 2a, 2b, 2c | 0, 1/2, 0 |
| Fdd2 (43) | <2 + (1, 1, 0); 3 + (0, 1, 0)> | 2a, 2b, 2c | 1/2, 1/2, 0 |
[3] a' = 3a
 | Pnn2 (34) | <2; 3 + (1, 0, 0)> | 3a, b, c | | | Pnn2 (34) | <2 + (2, 0, 0); 3 + (1, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pnn2 (34) | <2 + (4, 0, 0); 3 + (1, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pnn2 (34) | <2; 3 + (0, 1, 0)> | a, 3b, c | | | Pnn2 (34) | <2 + (0, 2, 0); 3 + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Pnn2 (34) | <2 + (0, 4, 0); 3 + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pnn2 (34) | <2; 3 + (0, 0, 1)> | a, b, 3c | |
- Series of maximal isomorphic subgroups
[p] a' = pa
| Pnn2 (34) | <2 + (2u, 0, 0); 3 + (p/2 - 1/2, 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
| Pnn2 (34) | <2 + (0, 2u, 0); 3 + (0, p/2 - 1/2 + 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
| Pnn2 (34) | <2; 3 + (0, 0, p/2 - 1/2)> | a, b, pc | | | | p > 2
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] Pnnn (48); [2] Pnna (52); [2] Pnnm (58); [2] P42nm (102); [2] P4nc (104); [2] P-4n2 (118) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Ccc2 (37); [2] Ama2 (40); [2] Bbm2 (40, Ama2); [2] Imm2 (44) |
| [2] a' = 1/2a Pnc2 (30); [2] b' = 1/2b Pcn2 (30, Pnc2); [2] c' = 1/2c Pba2 (32) |
