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) x, y(2) -y, x - y(3) -x + y, -x
(4) y, x(5) x - y, -y(6) -x, -x + y

I Maximal translationengleiche subgroups

[2] p311 (13, p3)1; 2; 3
brace[3] p11m (5, cm)1; 4 a - b,  a + b
[3] p11m (5, cm)1; 5 a + 2b, -a
[3] p11m (5, cm)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, pbu, v
 p > 1; p ≠ 3; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p

I Minimal translationengleiche supergroups

[2] p6mm (17)

II Minimal non-isomorphic klassengleiche supergroups

[3] h31m (14, p3m1)
none








































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