Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (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] Pmm2 (25) | 1; 2; 7; 8 |
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| [2] Pm2m (25, Pmm2) | 1; 3; 6; 8 | c, a, b
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| [2] P2mm (25, Pmm2) | 1; 4; 6; 7 | b, c, a
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| [2] P222 (16) | 1; 2; 3; 4 |
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| [2] P112/m (10) | 1; 2; 5; 6 |
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| [2] P12/m1 (10) | 1; 3; 5; 7 |
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| [2] P2/m11 (10, P12/m1) | 1; 4; 5; 8 | c, a, b
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II Maximal klassengleiche subgroups
[2] a' = 2a
| Pmma (51) | <3; 5; 2 + (1, 0, 0)> | 2a, b, c | |
| Pmma (51) | <2; (3; 5) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| Pmam (51, Pmma) | <2; 5; 3 + (1, 0, 0)> | 2a, -c, b | |
| Pmam (51, Pmma) | <3; (2; 5) + (1, 0, 0)> | 2a, -c, b | 1/2, 0, 0 |
| Pmaa (49, Pccm) | <5; (2; 3) + (1, 0, 0)> | b, c, 2a | |
| Pmaa (49, Pccm) | <2; 3; 5 + (1, 0, 0)> | b, c, 2a | 1/2, 0, 0 |
| Pmmm (47) | <2; 3; 5> | 2a, b, c | |
| Pmmm (47) | <(2; 3; 5) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| Pbmm (51, Pmma) | <2; 5; 3 + (0, 1, 0)> | 2b, c, a | |
| Pbmm (51, Pmma) | <(2; 3; 5) + (0, 1, 0)> | 2b, c, a | 0, 1/2, 0 |
| Pmmb (51, Pmma) | <5; (2; 3) + (0, 1, 0)> | -2b, a, c | |
| Pmmb (51, Pmma) | <2; (3; 5) + (0, 1, 0)> | -2b, a, c | 0, 1/2, 0 |
| Pbmb (49, Pccm) | <3; 5; 2 + (0, 1, 0)> | c, a, 2b | |
| Pbmb (49, Pccm) | <2; 3; 5 + (0, 1, 0)> | c, a, 2b | 0, 1/2, 0 |
| Pmmm (47) | <2; 3; 5> | a, 2b, c | |
| Pmmm (47) | <3; (2; 5) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] c' = 2c
| Pcmm (51, Pmma) | <3; 5; 2 + (0, 0, 1)> | 2c, b, -a | |
| Pcmm (51, Pmma) | <(2; 3; 5) + (0, 0, 1)> | 2c, b, -a | 0, 0, 1/2 |
| Pmcm (51, Pmma) | <5; (2; 3) + (0, 0, 1)> | 2c, a, b | |
| Pmcm (51, Pmma) | <3; (2; 5) + (0, 0, 1)> | 2c, a, b | 0, 0, 1/2 |
| Pccm (49) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Pccm (49) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pmmm (47) | <2; 3; 5> | a, b, 2c | |
| Pmmm (47) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] b' = 2b, c' = 2c
| Aemm (67, Cmme) | <3; 5; 2 + (0, 0, 1)> | 2b, 2c, a | |
| Aemm (67, Cmme) | <(2; 3; 5) + (0, 0, 1)> | 2b, 2c, a | 0, 0, 1/2 |
| Aemm (67, Cmme) | <2; 5; 3 + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 1/2 |
| Aemm (67, Cmme) | <2; 3; 5 + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 0 |
| Ammm (65, Cmmm) | <2; 3; 5> | 2b, 2c, a | |
| Ammm (65, Cmmm) | <2; (3; 5) + (0, 0, 1)> | 2b, 2c, a | 0, 0, 1/2 |
| Ammm (65, Cmmm) | <5; (2; 3) + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 1/2 |
| Ammm (65, Cmmm) | <3; (2; 5) + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 0 |
[2] a' = 2a, c' = 2c
| Bmem (67, Cmme) | <2; 5; 3 + (1, 0, 0)> | 2c, 2a, b | |
| Bmem (67, Cmme) | <3; (2; 5) + (1, 0, 0)> | 2c, 2a, b | 1/2, 0, 0 |
| Bmem (67, Cmme) | <5; (2; 3) + (1, 0, 0)> | 2c, 2a, b | 1/2, 0, 1/2 |
| Bmem (67, Cmme) | <2; 3; 5 + (1, 0, 0)> | 2c, 2a, b | 0, 0, 1/2 |
| Bmmm (65, Cmmm) | <2; 3; 5> | 2c, 2a, b | |
| Bmmm (65, Cmmm) | <(2; 3; 5) + (1, 0, 0)> | 2c, 2a, b | 1/2, 0, 0 |
| Bmmm (65, Cmmm) | <3; 5; 2 + (1, 0, 0)> | 2c, 2a, b | 1/2, 0, 1/2 |
| Bmmm (65, Cmmm) | <2; (3; 5) + (1, 0, 0)> | 2c, 2a, b | 0, 0, 1/2 |
[2] a' = 2a, b' = 2b
| Cmme (67) | <3; 5; 2 + (1, 0, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
| Cmme (67) | <2; (3; 5) + (1, 0, 0)> | 2a, 2b, c | 0, 1/2, 0 |
| Cmme (67) | <5; (2; 3) + (1, 0, 0)> | 2a, 2b, c | |
| Cmme (67) | <2; 3; 5 + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| Cmmm (65) | <2; 3; 5> | 2a, 2b, c | |
| Cmmm (65) | <(2; 3; 5) + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| Cmmm (65) | <2; 5; 3 + (1, 0, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
| Cmmm (65) | <3; (2; 5) + (1, 0, 0)> | 2a, 2b, c | 0, 1/2, 0 |
[2] a' = 2a, b' = 2b, c' = 2c
| Fmmm (69) | <2; 3; 5> | 2a, 2b, 2c | |
| Fmmm (69) | <(2; 3; 5) + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 0, 0 |
| Fmmm (69) | <3; 5; 2 + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 0, 1/2 |
| Fmmm (69) | <2; (3; 5) + (1, 0, 0)> | 2a, 2b, 2c | 0, 0, 1/2 |
| Fmmm (69) | <2; 5; 3 + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 1/2, 0 |
| Fmmm (69) | <3; (2; 5) + (1, 0, 0)> | 2a, 2b, 2c | 0, 1/2, 0 |
| Fmmm (69) | <5; (2; 3) + (1, 0, 0)> | 2a, 2b, 2c | 0, 1/2, 1/2 |
| Fmmm (69) | <2; 3; 5 + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 1/2, 1/2 |
[3] a' = 3a
 | Pmmm (47) | <2; 3; 5> | 3a, b, c | | | Pmmm (47) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pmmm (47) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pmmm (47) | <2; 3; 5> | a, 3b, c | | | Pmmm (47) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Pmmm (47) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pmmm (47) | <2; 3; 5> | a, b, 3c | | | Pmmm (47) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pmmm (47) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pmmm (47) | <(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
| Pmmm (47) | <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
| Pmmm (47) | <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] P4/mmm (123); [2] P42/mmc (131); [3] Pm-3 (200) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Ammm (65, Cmmm); [2] Bmmm (65, Cmmm); [2] Cmmm (65); [2] Immm (71) |
