Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); t(1/2, 0, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (0, 1/2, 1/2)+ (1/2, 0, 1/2)+ (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] F1m1 (8, C1m1) | (1; 3)+ | a, b, 1/2(-a + c)
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| [2] Fm11 (8, C1m1) | (1; 4)+ | c, a, 1/2(b - c)
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| [2] F112 (5, A112) | (1; 2)+ | 1/2(a - b), b, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Aea2 (41) | 1; 2; (1; 2) + (0, 1/2, 1/2); (3; 4) + (1/2, 0, 1/2); (3; 4) + (1/2, 1/2, 0) | | |
| [2] Bbe2 (41, Aea2) | 1; 2; (1; 2) + (1/2, 0, 1/2); (3; 4) + (0, 1/2, 1/2); (3; 4) + (1/2, 1/2, 0) | -b, a, c | |
| [2] Ama2 (40) | 1; 4; (1; 4) + (0, 1/2, 1/2); (2; 3) + (1/2, 0, 1/2); (2; 3) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] Bbm2 (40, Ama2) | 1; 3; (1; 3) + (1/2, 0, 1/2); (2; 4) + (0, 1/2, 1/2); (2; 4) + (1/2, 1/2, 0) | -b, a, c | 1/4, 1/4, 0 |
| [2] Bme2 (39, Aem2) | 1; 4; (1; 4) + (1/2, 0, 1/2); (2; 3) + (0, 1/2, 1/2); (2; 3) + (1/2, 1/2, 0) | -b, a, c | 1/4, 1/4, 0 |
| [2] Aem2 (39) | 1; 3; (1; 3) + (0, 1/2, 1/2); (2; 4) + (1/2, 0, 1/2); (2; 4) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] Amm2 (38) | 1; 2; 3; 4; (1; 2; 3; 4) + (0, 1/2, 1/2) | | |
| [2] Bmm2 (38, Amm2) | 1; 2; 3; 4; (1; 2; 3; 4) + (1/2, 0, 1/2) | -b, a, c | |
| [2] Ccc2 (37) | 1; 2; (1; 2) + (1/2, 1/2, 0); (3; 4) + (0, 1/2, 1/2); (3; 4) + (1/2, 0, 1/2) | | 1/4, 1/4, 0 |
| [2] Ccm21 (36, Cmc21) | 1; 3; (1; 3) + (1/2, 1/2, 0); (2; 4) + (0, 1/2, 1/2); (2; 4) + (1/2, 0, 1/2) | -b, a, c | 1/4, 0, 0 |
| [2] Cmc21 (36) | 1; 4; (1; 4) + (1/2, 1/2, 0); (2; 3) + (0, 1/2, 1/2); (2; 3) + (1/2, 0, 1/2) | | 0, 1/4, 0 |
| [2] Cmm2 (35) | 1; 2; 3; 4; (1; 2; 3; 4) + (1/2, 1/2, 0) | | |
[3] a' = 3a
 | Fmm2 (42) | <2; 3> | 3a, b, c | | | Fmm2 (42) | <3; 2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Fmm2 (42) | <3; 2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Fmm2 (42) | <2; 3> | a, 3b, c | | | Fmm2 (42) | <(2; 3) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Fmm2 (42) | <(2; 3) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
- Series of maximal isomorphic subgroups
[p] a' = pa
| Fmm2 (42) | <3; 2 + (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
| Fmm2 (42) | <(2; 3) + (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
| Fmm2 (42) | <2; 3> | a, b, pc | | | | p > 2
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] Fmmm (69); [2] I4mm (107); [2] I4cm (108); [2] I-42m (121) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c Pmm2 (25) |
