P4 No. 75 P4 C41

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

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

I Maximal translationengleiche subgroups

[2] P2 (3P112)1; 2

II Maximal klassengleiche subgroups

[2] c' = 2c

P42 (77)<2; 3 + (0, 0, 1)>ab, 2c
P4 (75)<2; 3>ab, 2c

[2] a' = 2a, b' = 2b

C4 (75, P4)<2; 3>a - ba + bc
C4 (75, P4)<2 + (1, 1, 0); 3 + (1, 0, 0)>a - ba + bc1/21/2, 0

[2] a' = 2a, b' = 2b, c' = 2c

F4 (79, I4)<2; 3>a - ba + b, 2c
F4 (79, I4)<2; 3 + (0, 0, 1)>a - ba + b, 2c1/21/2, 0

[3] c' = 3c

P4 (75)<2; 3>ab, 3c

[p] c' = pc


P4 (75)<2; 3>abpc
 p prime
no conjugate subgroups

[p2] a' = pa, b' = pb


P4 (75)<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


P4 (75)<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] P4/m (83); [2] P4/n (85); [2] P422 (89); [2] P4212 (90); [2] P4mm (99); [2] P4bm (100); [2] P4cc (103); [2] P4nc (104)

II Minimal non-isomorphic klassengleiche supergroups

[2] I4 (79)
none








































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