ORIGIN CHOICE 1, Origin at -4m 2, at 0, 1/4, -1/8 from centre (2/m)
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); (9)
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 + 1/2, -y + 1/2, z + 1/2 | (3) -y, x + 1/2, z + 1/4 | (4) y + 1/2, -x, z + 3/4 | | (5) -x + 1/2, y, -z + 3/4 | (6) x, -y + 1/2, -z + 1/4 | (7) y + 1/2, x + 1/2, -z + 1/2 | (8) -y, -x, -z | | (9) -x, -y + 1/2, -z + 1/4 | (10) x + 1/2, y, -z + 3/4 | (11) y, -x, -z | (12) -y + 1/2, x + 1/2, -z + 1/2 | | (13) x + 1/2, -y + 1/2, z + 1/2 | (14) -x, y, z | (15) -y + 1/2, -x, z + 3/4 | (16) y, x + 1/2, z + 1/4 |
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I Maximal translationengleiche subgroups
| [2] I-42d (122) | (1; 2; 5; 6; 11; 12; 15; 16)+ |
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| [2] I-4m2 (119) | (1; 2; 7; 8; 11; 12; 13; 14)+ |
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| [2] I41md (109) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
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| [2] I4122 (98) | (1; 2; 3; 4; 5; 6; 7; 8)+ |
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| [2] I41/a11 (88, I41/a) | (1; 2; 3; 4; 9; 10; 11; 12)+ |
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| [2] I2/a2/m1 (74, Imma) | (1; 2; 5; 6; 9; 10; 13; 14)+ |
| 0, 1/4, 1/8
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| [2] I2/a12/d (70, Fddd) | (1; 2; 7; 8; 9; 10; 15; 16)+ | a - b, a + b, c
| 0, 1/2, 1/4
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II Maximal klassengleiche subgroups
- Loss of centring translations
[3] c' = 3c
 | I41/amd (141) | <(2; 9) + (1, 0, 1); 3 + (1/2, -1/2, 1/2); 5 + (1, 0, 2)> | a, b, 3c | 1/2, 0, 1/4 | | I41/amd (141) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2); 5 + (1, 0, 4); 9 + (1, 0, 3)> | a, b, 3c | 1/2, 0, 5/4 | | I41/amd (141) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2); 5 + (1, 0, 6); 9 + (1, 0, 5)> | a, b, 3c | 1/2, 0, 9/4 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| I41/amd (141) | <2 + (1, 0, p/2 - 1/2); 3 + (1/2, -1/2, p/4 - 1/4); 5 + (1, 0, 3p/4 - 1/4 + 2u); 9 + (1, 0, p/4 + 1/4 + 2u)> | a, b, pc | 1/2, 0, 1/4 + u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| I41/amd (141) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/4 - 1/4); 5 + (0, 0, 3p/4 - 3/4 + 2u); 9 + (0, 0, p/4 - 1/4 + 2u)> | a, b, pc | 0, 0, u | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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[p2] a' = pa, b' = pb
| I41/amd (141) | <2 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0); 3 + (u + v, p/2 - 1/2 - u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 0); 9 + (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] c' = 1/2c C42/emd (134, P42/nnm) |
