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 + 1/2 | (4) x, -y, -z + 1/2 | | (5) -x, -y, -z | (6) x, y, -z | (7) x, -y, z + 1/2 | (8) -x, y, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] Pc2m (28, Pma2) | 1; 3; 6; 8 | c, a, b
| 0, 0, 1/4
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| [2] P2cm (28, Pma2) | 1; 4; 6; 7 | c, b, -a
| 0, 0, 1/4
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| [2] Pcc2 (27) | 1; 2; 7; 8 |
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| [2] P222 (16) | 1; 2; 3; 4 |
| 0, 0, 1/4
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| [2] P12/c1 (13) | 1; 3; 5; 7 |
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| [2] P2/c11 (13, P12/c1) | 1; 4; 5; 8 | -b, a, c
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| [2] P112/m (10) | 1; 2; 5; 6 |
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II Maximal klassengleiche subgroups
[2] a' = 2a
| Pcca (54) | <3; 5; 2 + (1, 0, 0)> | 2a, b, c | |
| Pcca (54) | <2; (3; 5) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| Pcnm (53, Pmna) | <2; 5; 3 + (1, 0, 0)> | c, b, -2a | |
| Pcnm (53, Pmna) | <3; (2; 5) + (1, 0, 0)> | c, b, -2a | 1/2, 0, 0 |
| Pcna (50, Pban) | <5; (2; 3) + (1, 0, 0)> | c, 2a, b | |
| Pcna (50, Pban) | <2; 3; 5 + (1, 0, 0)> | c, 2a, b | 1/2, 0, 0 |
| Pccm (49) | <2; 3; 5> | 2a, b, c | |
| Pccm (49) | <(2; 3; 5) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| Pccb (54, Pcca) | <5; (2; 3) + (0, 1, 0)> | -2b, a, c | |
| Pccb (54, Pcca) | <2; (3; 5) + (0, 1, 0)> | -2b, a, c | 0, 1/2, 0 |
| Pncm (53, Pmna) | <2; 5; 3 + (0, 1, 0)> | c, a, 2b | |
| Pncm (53, Pmna) | <(2; 3; 5) + (0, 1, 0)> | c, a, 2b | 0, 1/2, 0 |
| Pncb (50, Pban) | <3; 5; 2 + (0, 1, 0)> | 2b, c, a | |
| Pncb (50, Pban) | <2; 3; 5 + (0, 1, 0)> | 2b, c, a | 0, 1/2, 0 |
| Pccm (49) | <2; 3; 5> | a, 2b, c | |
| Pccm (49) | <3; (2; 5) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] a' = 2a, b' = 2b
| Ccce (68) | <3; 5; 2 + (1, 0, 0)> | 2a, 2b, c | |
| Ccce (68) | <5; (2; 3) + (1, 0, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
| Ccce (68) | <2; 3; 5 + (1, 0, 0)> | 2a, 2b, c | 0, 1/2, 0 |
| Ccce (68) | <2; (3; 5) + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| Cccm (66) | <2; 3; 5> | 2a, 2b, c | |
| Cccm (66) | <(2; 3; 5) + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| Cccm (66) | <2; 5; 3 + (1, 0, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
| Cccm (66) | <3; (2; 5) + (1, 0, 0)> | 2a, 2b, c | 0, 1/2, 0 |
[3] a' = 3a
 | Pccm (49) | <2; 3; 5> | 3a, b, c | | | Pccm (49) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pccm (49) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pccm (49) | <2; 3; 5> | a, 3b, c | | | Pccm (49) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Pccm (49) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pccm (49) | <2; 5; 3 + (0, 0, 1)> | a, b, 3c | | | Pccm (49) | <2; 3 + (0, 0, 3); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pccm (49) | <2; 3 + (0, 0, 5); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pccm (49) | <(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
| Pccm (49) | <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
| Pccm (49) | <2; 3 + (0, 0, p/2 - 1/2 + 2u); 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/mcc (124); [2] P42/mcm (132) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Cccm (66); [2] Aemm (67, Cmme); [2] Bmem (67, Cmme); [2] Ibam (72) |
