ORIGIN CHOICE 1, Origin at -4 2m, at -1/4, 1/4, -1/4 from centre (2/m)
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) -y + 1/2, x + 1/2, z + 1/2 | (4) y + 1/2, -x + 1/2, z + 1/2 | | (5) -x, y, -z | (6) x, -y, -z | (7) y + 1/2, x + 1/2, -z + 1/2 | (8) -y + 1/2, -x + 1/2, -z + 1/2 | | (9) -x + 1/2, -y + 1/2, -z + 1/2 | (10) x + 1/2, y + 1/2, -z + 1/2 | (11) y, -x, -z | (12) -y, x, -z | | (13) x + 1/2, -y + 1/2, z + 1/2 | (14) -x + 1/2, y + 1/2, z + 1/2 | (15) -y, -x, z | (16) y, x, z |
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I Maximal translationengleiche subgroups
| [2] P-4n2 (118) | 1; 2; 7; 8; 11; 12; 13; 14 |
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| [2] P-42m (111) | 1; 2; 5; 6; 11; 12; 15; 16 |
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| [2] P42nm (102) | 1; 2; 3; 4; 13; 14; 15; 16 |
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| [2] P4222 (93) | 1; 2; 3; 4; 5; 6; 7; 8 |
| 0, 1/2, 0
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| [2] P42/n11 (86, P42/n) | 1; 2; 3; 4; 9; 10; 11; 12 |
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| [2] P2/n12/m (67, Cmme) | 1; 2; 7; 8; 9; 10; 15; 16 | a - b, a + b, c
| 1/4, 1/4, 1/4
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| [2] P2/n2/n1 (48, Pnnn) | 1; 2; 5; 6; 9; 10; 13; 14 |
| 1/2, 1/2, 1/2
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| F41/ddc (142, I41/acd) | <2; 5; 9; 3 + (0, 0, 1)> | a - b, a + b, 2c | 1/2, 1/2, 0 |
| F41/ddc (142, I41/acd) | <2; (3; 5; 9) + (0, 0, 1)> | a - b, a + b, 2c | 1/2, 1/2, 1/2 |
| F41/ddc (142, I41/acd) | <2; 3; 9; 5 + (0, 0, 1)> | a - b, a + b, 2c | |
| F41/ddc (142, I41/acd) | <2; 3; 5; 9 + (0, 0, 1)> | a - b, a + b, 2c | 0, 0, 1/2 |
| F41/ddm (141, I41/amd) | <2; 9; (3; 5) + (0, 0, 1)> | a - b, a + b, 2c | 1/2, 1/2, 0 |
| F41/ddm (141, I41/amd) | <2; 5; (3; 9) + (0, 0, 1)> | a - b, a + b, 2c | 1/2, 1/2, 1/2 |
| F41/ddm (141, I41/amd) | <2; 3; 5; 9> | a - b, a + b, 2c | |
| F41/ddm (141, I41/amd) | <2; 3; (5; 9) + (0, 0, 1)> | a - b, a + b, 2c | 0, 0, 1/2 |
[3] c' = 3c
 | P42/nnm (134) | <2; 5; (3; 9) + (0, 0, 1)> | a, b, 3c | | | P42/nnm (134) | <2; 3 + (0, 0, 1); 5 + (0, 0, 2); 9 + (0, 0, 3)> | a, b, 3c | 0, 0, 1 | | P42/nnm (134) | <2; 3 + (0, 0, 1); 5 + (0, 0, 4); 9 + (0, 0, 5)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P42/nnm (134) | <2; 3 + (0, 0, p/2 - 1/2); 5 + (0, 0, 2u); 9 + (0, 0, p/2 - 1/2 + 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p2] a' = pa, b' = pb
| P42/nnm (134) | <2 + (2u, 2v, 0); 3 + (p/2 - 1/2 + u + v, p/2 - 1/2 - u + v, 0); 5 + (2u, 0, 0); 9 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C42/mcm (131, P42/mmc); [2] I4/mmm (139) |
| [2] c' = 1/2c P4/nbm (125) |
ORIGIN CHOICE 2, Origin at centre (2/m) at n n (21/g, 2/m), at 1/4, -1/4, 1/4 from -4 2 m
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z | (3) -y + 1/2, x, z + 1/2 | (4) y, -x + 1/2, z + 1/2 | | (5) -x + 1/2, y, -z + 1/2 | (6) x, -y + 1/2, -z + 1/2 | (7) y, x, -z | (8) -y + 1/2, -x + 1/2, -z | | (9) -x, -y, -z | (10) x + 1/2, y + 1/2, -z | (11) y + 1/2, -x, -z + 1/2 | (12) -y, x + 1/2, -z + 1/2 | | (13) x + 1/2, -y, z + 1/2 | (14) -x, y + 1/2, z + 1/2 | (15) -y, -x, z | (16) y + 1/2, x + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] P-4n2 (118) | 1; 2; 7; 8; 11; 12; 13; 14 |
| 1/4, 3/4, 1/4
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| [2] P-42m (111) | 1; 2; 5; 6; 11; 12; 15; 16 |
| 1/4, 3/4, 1/4
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| [2] P42nm (102) | 1; 2; 3; 4; 13; 14; 15; 16 |
| 1/4, 3/4, 0
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| [2] P4222 (93) | 1; 2; 3; 4; 5; 6; 7; 8 |
| 1/4, 1/4, 1/4
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| [2] P42/n11 (86, P42/n) | 1; 2; 3; 4; 9; 10; 11; 12 |
| 0, 1/2, 0
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| [2] P2/n12/m (67, Cmme) | 1; 2; 7; 8; 9; 10; 15; 16 | a - b, a + b, c
| 0, 1/2, 0
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| [2] P2/n2/n1 (48, Pnnn) | 1; 2; 5; 6; 9; 10; 13; 14 |
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| F41/ddc (142, I41/acd) | <5; 2 + (1, 0, 0); 3 + (0, 1, 1); 9 + (0, 1, 0)> | a - b, a + b, 2c | 0, 1/2, 0 |
| F41/ddc (142, I41/acd) | <2 + (1, 0, 0); (3; 9) + (0, 1, 1); 5 + (0, 0, 1)> | a - b, a + b, 2c | 0, 1/2, 1/2 |
| F41/ddc (142, I41/acd) | <2 + (1, 0, 0); (3; 9) + (0, 1, 0); 5 + (0, 0, 1)> | a - b, a + b, 2c | 1/2, 0, 0 |
| F41/ddc (142, I41/acd) | <5; 2 + (1, 0, 0); 3 + (0, 1, 0); 9 + (0, 1, 1)> | a - b, a + b, 2c | 1/2, 0, 1/2 |
| F41/ddm (141, I41/amd) | <2 + (1, 0, 0); 3 + (0, 1, 1); 5 + (0, 0, 1); 9 + (0, 1, 0)> | a - b, a + b, 2c | 0, 1/2, 0 |
| F41/ddm (141, I41/amd) | <5; 2 + (1, 0, 0); (3; 9) + (0, 1, 1)> | a - b, a + b, 2c | 0, 1/2, 1/2 |
| F41/ddm (141, I41/amd) | <5; 2 + (1, 0, 0); (3; 9) + (0, 1, 0)> | a - b, a + b, 2c | 1/2, 0, 0 |
| F41/ddm (141, I41/amd) | <2 + (1, 0, 0); 3 + (0, 1, 0); 5 + (0, 0, 1); 9 + (0, 1, 1)> | a - b, a + b, 2c | 1/2, 0, 1/2 |
[3] c' = 3c
| P42/nnm (134) | <2; 9; (3; 5) + (0, 0, 1)> | a, b, 3c | | | P42/nnm (134) | <2; 3 + (0, 0, 1); 5 + (0, 0, 3); 9 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P42/nnm (134) | <2; 3 + (0, 0, 1); 5 + (0, 0, 5); 9 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P42/nnm (134) | <2; 3 + (0, 0, p/2 - 1/2); 5 + (0, 0, p/2 - 1/2 + 2u); 9 + (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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[p2] a' = pa, b' = pb
| P42/nnm (134) | <2 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0); 3 + (p/2 - 1/2 + u + v, -u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 0); 9 + (2u, 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C42/mcm (131, P42/mmc); [2] I4/mmm (139) |
| [2] c' = 1/2c P4/nbm (125) |
