Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (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] P1m1 (6) | 1; 3 |
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| [2] Pm11 (6, P1m1) | 1; 4 | c, a, b
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| [2] P112 (3) | 1; 2 |
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II Maximal klassengleiche subgroups
[2] a' = 2a
| Pma2 (28) | <2; 3 + (1, 0, 0)> | 2a, b, c | |
| Pma2 (28) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
| Pmm2 (25) | <2; 3> | 2a, b, c | |
| Pmm2 (25) | <3; 2 + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| Pbm2 (28, Pma2) | <2; 3 + (0, 1, 0)> | -2b, a, c | |
| Pbm2 (28, Pma2) | <3; 2 + (0, 1, 0)> | -2b, a, c | 0, 1/2, 0 |
| Pmm2 (25) | <2; 3> | a, 2b, c | |
| Pmm2 (25) | <(2; 3) + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] c' = 2c
| Pcc2 (27) | <2; 3 + (0, 0, 1)> | a, b, 2c | |
| Pmc21 (26) | <(2; 3) + (0, 0, 1)> | a, b, 2c | |
| Pcm21 (26, Pmc21) | <3; 2 + (0, 0, 1)> | -b, a, 2c | |
| Pmm2 (25) | <2; 3> | a, b, 2c | |
[2] b' = 2b, c' = 2c
| Aem2 (39) | <2; 3 + (0, 1, 0)> | a, 2b, 2c | |
| Aem2 (39) | <3; 2 + (0, 1, 0)> | a, 2b, 2c | 0, 1/2, 0 |
| Amm2 (38) | <2; 3> | a, 2b, 2c | |
| Amm2 (38) | <(2; 3) + (0, 1, 0)> | a, 2b, 2c | 0, 1/2, 0 |
[2] a' = 2a, c' = 2c
| Bme2 (39, Aem2) | <2; 3 + (1, 0, 0)> | -b, 2a, 2c | |
| Bme2 (39, Aem2) | <(2; 3) + (1, 0, 0)> | -b, 2a, 2c | 1/2, 0, 0 |
| Bmm2 (38, Amm2) | <2; 3> | -b, 2a, 2c | |
| Bmm2 (38, Amm2) | <3; 2 + (1, 0, 0)> | -b, 2a, 2c | 1/2, 0, 0 |
[2] a' = 2a, b' = 2b
| Cmm2 (35) | <2; 3> | 2a, 2b, c | |
| Cmm2 (35) | <3; 2 + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| Cmm2 (35) | <(2; 3) + (0, 1, 0)> | 2a, 2b, c | 0, 1/2, 0 |
| Cmm2 (35) | <2 + (1, 1, 0); 3 + (0, 1, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
[2] a' = 2a, b' = 2b, c' = 2c
| Fmm2 (42) | <2; 3> | 2a, 2b, 2c | |
| Fmm2 (42) | <3; 2 + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 0, 0 |
| Fmm2 (42) | <(2; 3) + (0, 1, 0)> | 2a, 2b, 2c | 0, 1/2, 0 |
| Fmm2 (42) | <2 + (1, 1, 0); 3 + (0, 1, 0)> | 2a, 2b, 2c | 1/2, 1/2, 0 |
[3] a' = 3a
 | Pmm2 (25) | <2; 3> | 3a, b, c | | | Pmm2 (25) | <3; 2 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pmm2 (25) | <3; 2 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pmm2 (25) | <2; 3> | a, 3b, c | | | Pmm2 (25) | <(2; 3) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Pmm2 (25) | <(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
| Pmm2 (25) | <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
| Pmm2 (25) | <(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
| Pmm2 (25) | <2; 3> | a, b, pc | | | | p > 1
no conjugate subgroups |
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I Minimal translationengleiche supergroups
| [2] Pmmm (47); [2] Pmma (51); [2] Pmmn (59); [2] P4mm (99); [2] P42mc (105); [2] P-4m2 (115) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Cmm2 (35); [2] Amm2 (38); [2] Bmm2 (38, Amm2); [2] Imm2 (44) |
