P31m No. 157 P31m C3v2

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
6 d 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) yxz(5) x - y-yz(6) -x-x + yz

I Maximal translationengleiche subgroups

[2] P311 (143P3)1; 2; 3
brace[3] P11m (8C1m1)1; 4-a - ba - bc
[3] P11m (8C1m1)1; 5aa + 2bc
[3] P11m (8C1m1)1; 6b, -2a - bc

II Maximal klassengleiche subgroups

[2] c' = 2c

P31c (159)<2; 4 + (0, 0, 1)>ab, 2c
P31m (157)<2; 4>ab, 2c

[3] c' = 3c

P31m (157)<2; 4>ab, 3c

[3] a' = 3a, b' = 3b

H31m (156, P3m1)<2; 4>a - ba + 2bc

[3] a' = a - b, b' = a + 2b, c' = 3c

R3m (160)<2; 4>a - ba + 2b, 3c

[3] a' = 2a + b, b' = -a + b, c' = 3c

R3m (160)<2; 4>2a + b, -a + b, 3c

[4] a' = 2a, b' = 2b

braceP31m (157)<2; 4>2a, 2bc
P31m (157)<(2; 4) + (1, -1, 0)>2a, 2bc1, 0, 0
P31m (157)<2 + (1, 2, 0); 4 + (-1, 1, 0)>2a, 2bc0, 1, 0
P31m (157)<4; 2 + (2, 1, 0)>2a, 2bc1, 1, 0

[p] c' = pc


P31m (157)<2; 4>abpc
 p prime
no conjugate subgroups

[p2] a' = pa, b' = pb


P31m (157)<2 + (u + v, -u + 2v, 0); 4 + (u - v, -u + v, 0)>papbcuv, 0
 prime p ≠ 3; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups

[2] P-31m (162); [2] P6mm (183); [2] P63cm (185); [2] P-62m (189)

II Minimal non-isomorphic klassengleiche supergroups

[3] H31m (156, P3m1)
none








































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