Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3); (5)
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 + 1/2 | (3) -x, y, -z + 1/2 | (4) x, -y, -z | | (5) -x, -y, -z | (6) x, y, -z + 1/2 | (7) x, -y, z + 1/2 | (8) -x, y, z |
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I Maximal translationengleiche subgroups
| [2] C2cm (40, Ama2) | (1; 4; 6; 7)+ | c, b, -a
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| [2] Cm2m (38, Amm2) | (1; 3; 6; 8)+ | c, a, b
| 0, 0, 1/4
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| [2] Cmc21 (36) | (1; 2; 7; 8)+ |
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| [2] C2221 (20) | (1; 2; 3; 4)+ |
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| [2] C12/c1 (15) | (1; 3; 5; 7)+ |
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| [2] C2/m11 (12, C12/m1) | (1; 4; 5; 8)+ | -b, a, c
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| [2] C1121/m (11, P1121/m) | (1; 2; 5; 6)+ | 1/2(a - b), 1/2(a + b), c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pbnm (62, Pnma) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 0) | b, c, a | |
| [2] Pmcn (62, Pnma) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 0) | c, a, b | 1/4, 1/4, 0 |
| [2] Pbcn (60) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 0) | | |
| [2] Pmnm (59, Pmmn) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 0) | c, a, b | 1/4, 1/4, 0 |
| [2] Pmnn (58, Pnnm) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 0) | b, c, a | |
| [2] Pbcm (57) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] Pbnn (52, Pnna) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 0) | b, c, a | 1/4, 1/4, 0 |
| [2] Pmcm (51, Pmma) | 1; 2; 3; 4; 5; 6; 7; 8 | c, a, b | |
[3] a' = 3a
 | Cmcm (63) | <2; 3; 5> | 3a, b, c | | | Cmcm (63) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Cmcm (63) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Cmcm (63) | <2; 3; 5> | a, 3b, c | | | Cmcm (63) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Cmcm (63) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Cmcm (63) | <5; (2; 3) + (0, 0, 1)> | a, b, 3c | | | Cmcm (63) | <2 + (0, 0, 1); 3 + (0, 0, 3); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Cmcm (63) | <2 + (0, 0, 1); 3 + (0, 0, 5); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Cmcm (63) | <(2; 3; 5) + (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
| Cmcm (63) | <3; (2; 5) + (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
| Cmcm (63) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/2 - 1/2 + 2u); 5 + (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
| [3] P63/mcm (193); [3] P63/mmc (194) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b Pmcm (51, Pmma); [2] c' = 1/2c Cmmm (65) |
