c2mm No. 9 c2mm

Generators selected (1); t(1, 0); t(0, 1); t(1/21/2); (2); (3)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

(0, 0)+  (1/21/2)+
 8 f 1
 (1) x, y (2) -x, -y (3) -x, y (4) x, -y

I Maximal translationengleiche subgroups

 [2] c1m1 (5, cm) (1; 3)+ [2] c11m (5, cm) (1; 4)+ b, -a [2] c211 (2, p2) (1; 2)+ 1/2(a - b), 1/2(a + b)

II Maximal klassengleiche subgroups

• Loss of centring translations

 [2] p2gg (8) 1; 2; (3; 4) + (1/2, 1/2) [2] p2gm (7, p2mg) 1; 4; (2; 3) + (1/2, 1/2) b, -a 1/4, 1/4 [2] p2mg (7) 1; 3; (2; 4) + (1/2, 1/2) 1/4, 1/4 [2] p2mm (6) 1; 2; 3; 4
• Enlarged unit cell

[3] a' = 3a

 c2mm (9) <2; 3> 3a, b c2mm (9) <(2; 3) + (2, 0)> 3a, b 1, 0 c2mm (9) <(2; 3) + (4, 0)> 3a, b 2, 0

[3] b' = 3b

 c2mm (9) <2; 3> a, 3b c2mm (9) <3; 2 + (0, 2)> a, 3b 0, 1 c2mm (9) <3; 2 + (0, 4)> a, 3b 0, 2
• Series of maximal isomorphic subgroups

[p] a' = pa

 c2mm (9) <(2; 3) + (2u, 0)> pa, b u, 0 p > 2; 0 ≤ u < p p conjugate subgroups for the prime p

[p] b' = pb

 c2mm (9) <3; 2 + (0, 2u)> a, pb 0, u p > 2; 0 ≤ u < p p conjugate subgroups for the prime p

I Minimal translationengleiche supergroups

 [2] p4mm (11); [2] p4gm (12); [3] p6mm (17)

II Minimal non-isomorphic klassengleiche supergroups