p31m No. 15 p31m

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
6 d 1
(1) xy(2) -yx - y(3) -x + y-x
(4) yx(5) x - y-y(6) -x-x + y

I Maximal translationengleiche subgroups


[2] p311 (13p3)1; 2; 3
brace[3] p11m (5cm)1; 4 a - ba + b
[3] p11m (5cm)1; 5 a + 2b, -a
[3] p11m (5cm)1; 6-2a - b, -b

II Maximal klassengleiche subgroups

[3] a' = 3a, b' = 3b


h31m (14, p3m1)<2; 4>a - b, a + 2b

[4] a' = 2a, b' = 2b


bracep31m (15)<2; 4>2a, 2b
p31m (15)<(2; 4) + (1, -1)>2a, 2b1, 0
p31m (15)<2 + (1, 2); 4 + (-1, 1)>2a, 2b0, 1
p31m (15)<4; 2 + (2, 1)>2a, 2b1, 1

[p2] a' = pa, b' = pb


p31m (15)<2 + (u + v, -u + 2v); 4 + (u - v, -u + v)>pa, pbuv
 p prime; p ≠ 3; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups


[2] p6mm (17)

II Minimal non-isomorphic klassengleiche supergroups


[3] h31m (14, p3m1)

none








































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