Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (0, 1/2, 1/2)+ |
| | (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] A1m1 (8, C1m1) | (1; 3)+ | c, b, -a - c
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| [2] Am11 (6, P1m1) | (1; 4)+ | 1/2(b + c), a, 1/2(b - c)
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| [2] A112 (5) | (1; 2)+ |
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pnm21 (31, Pmn21) | 1; 3; (2; 4) + (0, 1/2, 1/2) | -b, a, c | |
| [2] Pnc2 (30) | 1; 2; (3; 4) + (0, 1/2, 1/2) | | |
| [2] Pmc21 (26) | 1; 4; (2; 3) + (0, 1/2, 1/2) | | 0, 1/4, 0 |
| [2] Pmm2 (25) | 1; 2; 3; 4 | | |
[2] a' = 2a
| Ima2 (46) | <2; 3 + (1, 0, 0)> | 2a, b , c | |
| Ima2 (46) | <(2; 3) + (1, 0, 0)> | 2a, b , c | 1/2, 0, 0 |
| Imm2 (44) | <2; 3> | 2a, b , c | |
| Imm2 (44) | <3; 2 + (1, 0, 0)> | 2a, b , c | 1/2, 0, 0 |
| Ama2 (40) | <2; 3 + (1, 0, 0)> | 2a, b , c | |
| Ama2 (40) | <(2; 3) + (1, 0, 0)> | 2a, b , c | 1/2, 0, 0 |
| Amm2 (38) | <2; 3> | 2a, b, c | |
| Amm2 (38) | <3; 2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[3] a' = 3a
 | Amm2 (38) | <2; 3> | 3a, b, c | | | Amm2 (38) | <3; 2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Amm2 (38) | <3; 2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Amm2 (38) | <2; 3> | a, 3b, c | | | Amm2 (38) | <(2; 3) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Amm2 (38) | <(2; 3) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
- Series of maximal isomorphic subgroups
[p] a' = pa
| Amm2 (38) | <3; 2 + (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
| Amm2 (38) | <(2; 3) + (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
| Amm2 (38) | <2; 3> | a, b, pc | | | | p > 2
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] Cmcm (63); [2] Cmmm (65); [3] P-6m2 (187); [3] P-62m (189) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] b' = 1/2b, c' = 1/2c Pmm2 (25) |
