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, -y, z | (3) -y, x, z | (4) y, -x, z | (5) -x, y, -z + 1/2 | (6) x, -y, -z + 1/2 | (7) y, x, -z + 1/2 | (8) -y, -x, -z + 1/2 | (9) -x, -y, -z | (10) x, y, -z | (11) y, -x, -z | (12) -y, x, -z | (13) x, -y, z + 1/2 | (14) -x, y, z + 1/2 | (15) -y, -x, z + 1/2 | (16) y, x, z + 1/2 |
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I Maximal translationengleiche subgroups
[2] I-42m (121) | (1; 2; 5; 6; 11; 12; 15; 16)+ |
| 0, 1/2, 1/4
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[2] I-4c2 (120) | (1; 2; 7; 8; 11; 12; 13; 14)+ |
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[2] I4cm (108) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
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[2] I422 (97) | (1; 2; 3; 4; 5; 6; 7; 8)+ |
| 0, 0, 1/4
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[2] I4/m11 (87, I4/m) | (1; 2; 3; 4; 9; 10; 11; 12)+ |
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[2] I2/m2/c1 (72, Ibam) | (1; 2; 5; 6; 9; 10; 13; 14)+ |
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[2] I2/m12/m (69, Fmmm) | (1; 2; 7; 8; 9; 10; 15; 16)+ | a - b, a + b, c
| 0, 1/2, 0
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II Maximal klassengleiche subgroups
- Loss of centring translations
[2] P42/ncm (138) | 1; 2; 7; 8; 11; 12; 13; 14; (3; 4; 5; 6; 9; 10; 15; 16) + (1/2, 1/2, 1/2) | | 1/4, 3/4, 1/4 |
[2] P42/mbc (135) | 1; 2; 7; 8; 9; 10; 15; 16; (3; 4; 5; 6; 11; 12; 13; 14) + (1/2, 1/2, 1/2) | | 0, 1/2, 0 |
[2] P42/nbc (133) | 1; 2; 5; 6; 11; 12; 15; 16; (3; 4; 7; 8; 9; 10; 13; 14) + (1/2, 1/2, 1/2) | | 1/4, 3/4, 1/4 |
[2] P42/mcm (132) | 1; 2; 5; 6; 9; 10; 13; 14; (3; 4; 7; 8; 11; 12; 15; 16) + (1/2, 1/2, 1/2) | | 0, 1/2, 0 |
[2] P4/ncc (130) | 1; 2; 3; 4; 13; 14; 15; 16; (5; 6; 7; 8; 9; 10; 11; 12) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
[2] P4/mbm (127) | 1; 2; 3; 4; 9; 10; 11; 12; (5; 6; 7; 8; 13; 14; 15; 16) + (1/2, 1/2, 1/2) | | |
[2] P4/nbm (125) | 1; 2; 3; 4; 5; 6; 7; 8; (9; 10; 11; 12; 13; 14; 15; 16) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
[2] P4/mcc (124) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16 | | |
[3] c' = 3c
| I4/mcm (140) | <2; 3; 9; 5 + (0, 0, 1)> | a, b, 3c | | I4/mcm (140) | <2; 3; 5 + (0, 0, 3); 9 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | I4/mcm (140) | <2; 3; 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
I4/mcm (140) | <2; 3; 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
I4/mcm (140) | <(2; 9) + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 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 C4/mmm (123, P4/mmm) |