I4 No. 79 I4 C45

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 c 1
(1) xyz(2) -x-yz(3) -yxz(4) y-xz

I Maximal translationengleiche subgroups

[2] I2 (5A112)(1; 2)+b, -a - bc

II Maximal klassengleiche subgroups

[2] P42 (77)1; 2; (3; 4) + (1/21/21/2)1/2, 0, 0
[2] P4 (75)1; 2; 3; 4

[3] c' = 3c

I4 (79)<2; 3>ab, 3c

[p] c' = pc


I4 (79)<2; 3>abpc
 prime p > 2
no conjugate subgroups

[p2] a' = pa, b' = pb


I4 (79)<2 + (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 (79)<2 + (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/m (87); [2] I422 (97); [2] I4mm (107); [2] I4cm (108)

II Minimal non-isomorphic klassengleiche supergroups

none
[2] c' = 1/2c  C4 (75, P4)








































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