Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3); (5)
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, -y, z | (3) -x, y, -z | (4) x, -y, -z | | (5) -x, -y, -z | (6) x, y, -z | (7) x, -y, z | (8) -x, y, z |
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I Maximal translationengleiche subgroups
| [2] Imm2 (44) | (1; 2; 7; 8)+ |
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| [2] Im2m (44, Imm2) | (1; 3; 6; 8)+ | c, a, b
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| [2] I2mm (44, Imm2) | (1; 4; 6; 7)+ | b, c, a
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| [2] I222 (23) | (1; 2; 3; 4)+ |
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| [2] I112/m (12, A112/m) | (1; 2; 5; 6)+ | b, -a - b, c
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| [2] I12/m1 (12, C12/m1) | (1; 3; 5; 7)+ | -a - c, b, a
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| [2] I2/m11 (12, C12/m1) | (1; 4; 5; 8)+ | -b + c, a, b
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pmmn (59) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] Pmnm (59, Pmmn) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 1/2) | c, a, b | 1/4, 1/4, 1/4 |
| [2] Pnmm (59, Pmmn) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 1/2) | b, c, a | 1/4, 1/4, 1/4 |
| [2] Pnnm (58) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) | | |
| [2] Pnmn (58, Pnnm) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 1/2) | c, a, b | |
| [2] Pmnn (58, Pnnm) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 1/2) | b, c, a | |
| [2] Pnnn (48) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] Pmmm (47) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
[3] a' = 3a
 | Immm (71) | <2; 3; 5> | 3a, b, c | | | Immm (71) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Immm (71) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Immm (71) | <2; 3; 5> | a, 3b, c | | | Immm (71) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Immm (71) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Immm (71) | <2; 3; 5> | a, b, 3c | | | Immm (71) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Immm (71) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Immm (71) | <(2; 3; 5) + (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
| Immm (71) | <3; (2; 5) + (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
| Immm (71) | <2; (3; 5) + (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] I4/mmm (139); [3] Im-3 (204) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a Ammm (65, Cmmm); [2] b' = 1/2b Bmmm (65, Cmmm); [2] c' = 1/2c Cmmm (65) |
