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 | (3) -x, y, -z | (4) x, -y, -z | | (5) -x, -y, -z | (6) x, y, -z | (7) x, -y, z | (8) -x, y, z |
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I Maximal translationengleiche subgroups
| [2] Cm2m (38, Amm2) | (1; 3; 6; 8)+ | c, a, b
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| [2] C2mm (38, Amm2) | (1; 4; 6; 7)+ | c, b, -a
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| [2] Cmm2 (35) | (1; 2; 7; 8)+ |
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| [2] C222 (21) | (1; 2; 3; 4)+ |
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| [2] C12/m1 (12) | (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] C112/m (10, P112/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] Pmmn (59) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] Pbam (55) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 0) | | |
| [2] Pbmn (53, Pmna) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 0) | b, c, a | |
| [2] Pman (53, Pmna) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 0) | a, -c, b | |
| [2] Pmam (51, Pmma) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 0) | a, -c, b | 1/4, 1/4, 0 |
| [2] Pbmm (51, Pmma) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 0) | b, c, a | 1/4, 1/4, 0 |
| [2] Pban (50) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 0) | | 1/4, 1/4, 0 |
| [2] Pmmm (47) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
[2] c' = 2c
| Ibmm (74, Imma) | <3; 5; 2 + (0, 0, 1)> | b, 2c, a | |
| Ibmm (74, Imma) | <(2; 3; 5) + (0, 0, 1)> | b, 2c, a | 0, 0, 1/2 |
| Imam (74, Imma) | <5; (2; 3) + (0, 0, 1)> | a, -2c, b | |
| Imam (74, Imma) | <3; (2; 5) + (0, 0, 1)> | a, -2c, b | 0, 0, 1/2 |
| Ibam (72) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Ibam (72) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Immm (71) | <2; 3; 5> | a, b, 2c | |
| Immm (71) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Cccm (66) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Cccm (66) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Cmmm (65) | <2; 3; 5> | a, b, 2c | |
| Cmmm (65) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Ccmm (63, Cmcm) | <3; 5; 2 + (0, 0, 1)> | -b, a, 2c | |
| Ccmm (63, Cmcm) | <(2; 3; 5) + (0, 0, 1)> | -b, a, 2c | 0, 0, 1/2 |
| Cmcm (63) | <5; (2; 3) + (0, 0, 1)> | a, b, 2c | |
| Cmcm (63) | <3; (2; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a
 | Cmmm (65) | <2; 3; 5> | 3a, b, c | | | Cmmm (65) | <(2; 3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Cmmm (65) | <(2; 3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Cmmm (65) | <2; 3; 5> | a, 3b, c | | | Cmmm (65) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Cmmm (65) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Cmmm (65) | <2; 3; 5> | a, b, 3c | | | Cmmm (65) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Cmmm (65) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Cmmm (65) | <(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
| Cmmm (65) | <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
| Cmmm (65) | <2; (3; 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
| [2] P4/mmm (123); [2] P4/mbm (127); [2] P42/mcm (132); [2] P42/mnm (136); [3] P6/mmm (191) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b Pmmm (47) |
