I4/m No. 87 I4/m C4h5

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/21/2); (2); (3); (5)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 (0, 0, 0)+  (1/21/21/2)+  
16 i 1
(1) xyz(2) -x-yz(3) -yxz(4) y-xz
(5) -x-y-z(6) xy-z(7) y-x-z(8) -yx-z

I Maximal translationengleiche subgroups

[2] I-4 (82)(1; 2; 7; 8)+
[2] I4 (79)(1; 2; 3; 4)+
[2] I2/m (12A112/m)(1; 2; 5; 6)+b, -a - bc

II Maximal klassengleiche subgroups

[2] P42/n (86)1; 2; 7; 8; (3; 4; 5; 6) + (1/21/21/2)1/41/41/4
[2] P4/n (85)1; 2; 3; 4; (5; 6; 7; 8) + (1/21/21/2)1/41/41/4
[2] P42/m (84)1; 2; 5; 6; (3; 4; 7; 8) + (1/21/21/2)0, 1/2, 0
[2] P4/m (83)1; 2; 3; 4; 5; 6; 7; 8

[3] c' = 3c

braceI4/m (87)<2; 3; 5>ab, 3c
I4/m (87)<2; 3; 5 + (0, 0, 2)>ab, 3c0, 0, 1
I4/m (87)<2; 3; 5 + (0, 0, 4)>ab, 3c0, 0, 2

[p] c' = pc


I4/m (87)<2; 3; 5 + (0, 0, 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p2] a' = pa, b' = pb


I4/m (87)<(2; 5) + (2u, 2v, 0); 3 + (u + v, -u + v, 0)>papbcuv, 0
 prime p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for p = 4n - 1

[p = q2 + r2] a' = qa - rb, b' = ra + qb


I4/m (87)<(2; 5) + (2u, 0, 0); 3 + (u, -u, 0)>qa - rbra + qbcu, 0, 0
 prime p > 4; q > 0; r > 0; 0 ≤ u < p
p conjugate subgroups for p = 4n + 1

I Minimal translationengleiche supergroups

[2] I4/mmm (139); [2] I4/mcm (140)

II Minimal non-isomorphic klassengleiche supergroups

none
[2] c' = 1/2c  C4/m (83, P4/m)








































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