Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z |
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I Maximal translationengleiche subgroups
| [2] C121 (5) | (1; 3)+ |
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| [2] C211 (5, C121) | (1; 4)+ | -b, a, c
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| [2] C112 (3, P112) | (1; 2)+ | 1/2(a - b), 1/2(a + b), c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P21212 (18) | 1; 2; (3; 4) + (1/2, 1/2, 0) | | |
| [2] P2122 (17, P2221) | 1; 3; (2; 4) + (1/2, 1/2, 0) | b, c, a | 0, 1/4, 0 |
| [2] P2212 (17, P2221) | 1; 4; (2; 3) + (1/2, 1/2, 0) | c, a, b | 1/4, 1/4, 0 |
| [2] P222 (16) | 1; 2; 3; 4 | | |
[2] c' = 2c
| I212121 (24) | <3; 2 + (0, 0, 1)> | a, b, 2c | 3/4, 0, 0 |
| I212121 (24) | <(2; 3) + (0, 0, 1)> | a, b, 2c | 3/4, 0, 1/2 |
| I222 (23) | <2; 3> | a, b, 2c | |
| I222 (23) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| C222 (21) | <2; 3> | a, b, 2c | |
| C222 (21) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| C2221 (20) | <3; 2 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| C2221 (20) | <(2; 3) + (0, 0, 1)> | a, b, 2c | |
[3] a' = 3a
 | C222 (21) | <2; 3> | 3a, b, c | | | C222 (21) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | C222 (21) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| C222 (21) | <2; 3> | a, 3b, c | | | C222 (21) | <3; 2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | C222 (21) | <3; 2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| C222 (21) | <2; 3> | a, b, 3c | | | C222 (21) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | C222 (21) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| C222 (21) | <(2; 3) + (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
| C222 (21) | <3; 2 + (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
| C222 (21) | <2; 3 + (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] Cmmm (65); [2] Cccm (66); [2] Cmme (67); [2] Ccce (68); [2] P422 (89); [2] P4212 (90); [2] P4222 (93); [2] P42212 (94); [2] P-4m2 (115); [2] P-4c2 (116); [2] P-4b2 (117); [2] P-4n2 (118); [3] P622 (177); [3] P6222 (180); [3] P6422 (181) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b P222 (16) |
