I222 No. 23 I222 D28

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 (0, 0, 0)+  (1/21/21/2)+  
8 k 1
(1) xyz(2) -x-yz(3) -xy-z(4) x-y-z

I Maximal translationengleiche subgroups

[2] I112 (5A112)(1; 2)+b, -a - bc
[2] I121 (5C121)(1; 3)+-a - cba
[2] I211 (5C121)(1; 4)+-b - cac

II Maximal klassengleiche subgroups

[2] P21212 (18)1; 2; (3; 4) + (1/21/21/2)0, 0, 1/4
[2] P21221 (18P21212)1; 3; (2; 4) + (1/21/21/2)cab0, 1/4, 0
[2] P22121 (18P21212)1; 4; (2; 3) + (1/21/21/2)bca1/4, 0, 0
[2] P222 (16)1; 2; 3; 4

[3] a' = 3a

braceI222 (23)<2; 3>3abc
I222 (23)<(2; 3) + (2, 0, 0)>3abc1, 0, 0
I222 (23)<(2; 3) + (4, 0, 0)>3abc2, 0, 0

[3] b' = 3b

braceI222 (23)<2; 3>a, 3bc
I222 (23)<3; 2 + (0, 2, 0)>a, 3bc0, 1, 0
I222 (23)<3; 2 + (0, 4, 0)>a, 3bc0, 2, 0

[3] c' = 3c

braceI222 (23)<2; 3>ab, 3c
I222 (23)<2; 3 + (0, 0, 2)>ab, 3c0, 0, 1
I222 (23)<2; 3 + (0, 0, 4)>ab, 3c0, 0, 2

[p] a' = pa


I222 (23)<(2; 3) + (2u, 0, 0)>pabcu, 0, 0
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p] b' = pb


I222 (23)<3; 2 + (0, 2u, 0)>apbc0, u, 0
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p] c' = pc


I222 (23)<2; 3 + (0, 0, 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

I Minimal translationengleiche supergroups

[2] Immm (71); [2] Ibam (72); [2] I422 (97); [2] I-42m (121); [3] I23 (197)

II Minimal non-isomorphic klassengleiche supergroups

none
[2] a' = 1/2a  A222 (21, C222); [2] b' = 1/2b  B222 (21, C222); [2] c' = 1/2c  C222 (21)








































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