P31 No. 144 P31 C32

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
3 a 1
(1) xyz(2) -yx - yz + 1/3(3) -x + y-xz + 2/3

I Maximal translationengleiche subgroups

[3] P1 (1)1

II Maximal klassengleiche subgroups

[2] c' = 2c

P32 (145)<2 + (0, 0, 1)>ab, 2c

[3] a' = 3a, b' = 3b

H31 (144, P31)<2>a - ba + 2bc
H31 (144, P31)<2 + (1, 0, 0)>a - ba + 2bc2/31/3, 0
H31 (144, P31)<2 + (1, 1, 0)>a - ba + 2bc1/32/3, 0

[4] a' = 2a, b' = 2b

braceP31 (144)<2>2a, 2bc
P31 (144)<2 + (1, -1, 0)>2a, 2bc1, 0, 0
P31 (144)<2 + (1, 2, 0)>2a, 2bc0, 1, 0
P31 (144)<2 + (2, 1, 0)>2a, 2bc1, 1, 0

[p] c' = pc


P32 (145)<2 + (0, 0, 2p/3 - 1/3)>abpc
 p prime; p = 2 or p = 6n - 1
no conjugate subgroups
P31 (144)<2 + (0, 0, p/3 - 1/3)>abpc
 prime p = 6n + 1
no conjugate subgroups

[p2] a' = pa, b' = pb


P31 (144)<2 + (u + v, -u + 2v, 0)>papbcuv, 0
 p prime; p = 2 or p = 6n - 1; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

[p = q2 + r2 + qr] a' = qa - rb, b' = ra + (q + r)b


P31 (144)<2 + (u, -u, 0)>qa - rbra + (q + r)bcu, 0, 0
 prime p > 6; q > 0; r > 0; 0 ≤ u < p
p conjugate subgroups for each pair of q and r

I Minimal translationengleiche supergroups

[2] P3112 (151); [2] P3121 (152); [2] P61 (169); [2] P64 (172)

II Minimal non-isomorphic klassengleiche supergroups

[3] R3 (obverse) (146, R3); [3] R3 (reverse) (146, R3)
[3] c' = 1/3c  P3 (143)








































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