ORIGIN CHOICE 1, Origin at m m 2/n, at 1/4, 1/4, 0 from -1
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | |
| | (1) x, y, z | (2) -x, -y, z | (3) -x + 1/2, y + 1/2, -z | (4) x + 1/2, -y + 1/2, -z | | (5) -x + 1/2, -y + 1/2, -z | (6) x + 1/2, y + 1/2, -z | (7) x, -y, z | (8) -x, y, z |
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I Maximal translationengleiche subgroups
| [2] Pm21n (31, Pmn21) | 1; 3; 6; 8 | a, -c, b
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| [2] P21mn (31, Pmn21) | 1; 4; 6; 7 | b, c, a
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| [2] Pmm2 (25) | 1; 2; 7; 8 |
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| [2] P21212 (18) | 1; 2; 3; 4 |
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| [2] P112/n (13, P112/a) | 1; 2; 5; 6 | -a - b, a, c
| 1/4, 1/4, 0
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| [2] P121/m1 (11) | 1; 3; 5; 7 |
| 1/4, 1/4, 0
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| [2] P21/m11 (11, P121/m1) | 1; 4; 5; 8 | c, a, b
| 1/4, 1/4, 0
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II Maximal klassengleiche subgroups
[2] c' = 2c
| Pcmn (62, Pnma) | <3; 5; 2 + (0, 0, 1)> | 2c, b, -a | 1/4, 1/4, 0 |
| Pcmn (62, Pnma) | <(2; 3; 5) + (0, 0, 1)> | 2c, b, -a | 1/4, 1/4, 1/2 |
| Pmcn (62, Pnma) | <5; (2; 3) + (0, 0, 1)> | 2c, a, b | 1/4, 1/4, 0 |
| Pmcn (62, Pnma) | <3; (2; 5) + (0, 0, 1)> | 2c, a, b | 1/4, 1/4, 1/2 |
| Pmmn (59) | <2; 3; 5> | a, b, 2c | |
| Pmmn (59) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pccn (56) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | 1/4, 1/4, 0 |
| Pccn (56) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 1/4, 1/4, 1/2 |
[3] a' = 3a
 | Pmmn (59) | <2; (3; 5) + (1, 0, 0)> | 3a, b, c | | | Pmmn (59) | <2 + (2, 0, 0); (3; 5) + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pmmn (59) | <2 + (4, 0, 0); (3; 5) + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pmmn (59) | <2; (3; 5) + (0, 1, 0)> | a, 3b, c | | | Pmmn (59) | <2 + (0, 2, 0); 3 + (0, 1, 0); 5 + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Pmmn (59) | <2 + (0, 4, 0); 3 + (0, 1, 0); 5 + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pmmn (59) | <2; 3; 5> | a, b, 3c | | | Pmmn (59) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pmmn (59) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pmmn (59) | <2 + (2u, 0, 0); (3; 5) + (p/2 - 1/2 + 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
| Pmmn (59) | <2 + (0, 2u, 0); 3 + (0, p/2 - 1/2, 0); 5 + (0, p/2 - 1/2 + 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
| Pmmn (59) | <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/nmm (129); [2] P42/nmc (137) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Amma (63, Cmcm); [2] Bmmb (63, Cmcm); [2] Cmmm (65); [2] Immm (71) |
| [2] a' = 1/2a Pmmb (51, Pmma); [2] b' = 1/2b Pmma (51) |
ORIGIN CHOICE 2, Origin at -1 at 21 21 n, at -1/4, -1/4, 0 from m m 2
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z | (3) -x, y + 1/2, -z | (4) x + 1/2, -y, -z | | (5) -x, -y, -z | (6) x + 1/2, y + 1/2, -z | (7) x, -y + 1/2, z | (8) -x + 1/2, y, z |
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I Maximal translationengleiche subgroups
| [2] Pm21n (31, Pmn21) | 1; 3; 6; 8 | a, -c, b
| 1/4, 1/4, 0
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| [2] P21mn (31, Pmn21) | 1; 4; 6; 7 | b, c, a
| 1/4, 1/4, 0
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| [2] Pmm2 (25) | 1; 2; 7; 8 |
| 1/4, 1/4, 0
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| [2] P21212 (18) | 1; 2; 3; 4 |
| 1/4, 1/4, 0
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| [2] P112/n (13, P112/a) | 1; 2; 5; 6 | -a - b, a, c
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| [2] P121/m1 (11) | 1; 3; 5; 7 |
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| [2] P21/m11 (11, P121/m1) | 1; 4; 5; 8 | c, a, b
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II Maximal klassengleiche subgroups
[2] c' = 2c
| Pcmn (62, Pnma) | <3; 5; 2 + (0, 0, 1)> | 2c, b, -a | |
| Pcmn (62, Pnma) | <(2; 3; 5) + (0, 0, 1)> | 2c, b, -a | 0, 0, 1/2 |
| Pmcn (62, Pnma) | <5; (2; 3) + (0, 0, 1)> | 2c, a, b | |
| Pmcn (62, Pnma) | <3; (2; 5) + (0, 0, 1)> | 2c, a, b | 0, 0, 1/2 |
| Pmmn (59) | <2; 3; 5> | a, b, 2c | |
| Pmmn (59) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pccn (56) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Pccn (56) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a
| Pmmn (59) | <3; 5; 2 + (1, 0, 0)> | 3a, b, c | | | Pmmn (59) | <2 + (3, 0, 0); (3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pmmn (59) | <2 + (5, 0, 0); (3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pmmn (59) | <5; (2; 3) + (0, 1, 0)> | a, 3b, c | | | Pmmn (59) | <2 + (0, 3, 0); 3 + (0, 1, 0); 5 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Pmmn (59) | <2 + (0, 5, 0); 3 + (0, 1, 0); 5 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pmmn (59) | <2; 3; 5> | a, b, 3c | | | Pmmn (59) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pmmn (59) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pmmn (59) | <2 + (p/2 - 1/2 + 2u, 0, 0); (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
| Pmmn (59) | <2 + (0, p/2 - 1/2 + 2u, 0); 3 + (0, p/2 - 1/2, 0); 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
| Pmmn (59) | <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/nmm (129); [2] P42/nmc (137) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Amma (63, Cmcm); [2] Bmmb (63, Cmcm); [2] Cmmm (65); [2] Immm (71) |
| [2] a' = 1/2a Pmmb (51, Pmma); [2] b' = 1/2b Pmma (51) |
