P4/nnc No. 126 P4/n2/n2/c D4h4

ORIGIN CHOICE 1, Origin at 4 2 2/n, at -1/4, -1/4, -1/4 from -1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (9)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
16 k 1
(1) xyz(2) -x-yz(3) -yxz(4) y-xz
(5) -xy-z(6) x-y-z(7) yx-z(8) -y-x-z
(9) -x + 1/2-y + 1/2-z + 1/2(10) x + 1/2y + 1/2-z + 1/2(11) y + 1/2-x + 1/2-z + 1/2(12) -y + 1/2x + 1/2-z + 1/2
(13) x + 1/2-y + 1/2z + 1/2(14) -x + 1/2y + 1/2z + 1/2(15) -y + 1/2-x + 1/2z + 1/2(16) y + 1/2x + 1/2z + 1/2

I Maximal translationengleiche subgroups

[2] P-4n2 (118)1; 2; 7; 8; 11; 12; 13; 14 0, 1/21/4
[2] P-42c (112)1; 2; 5; 6; 11; 12; 15; 16 0, 1/21/4
[2] P4nc (104)1; 2; 3; 4; 13; 14; 15; 16
[2] P422 (89)1; 2; 3; 4; 5; 6; 7; 8
[2] P4/n11 (85P4/n)1; 2; 3; 4; 9; 10; 11; 12 0, 1/21/4
[2] P2/n12/c (68Ccce)1; 2; 7; 8; 9; 10; 15; 16a - ba + bc
[2] P2/n2/n1 (48Pnnn)1; 2; 5; 6; 9; 10; 13; 14

II Maximal klassengleiche subgroups

[3] c' = 3c

braceP4/nnc (126)<2; 3; 5; 9 + (0, 0, 1)>ab, 3c
P4/nnc (126)<2; 3; 5 + (0, 0, 2); 9 + (0, 0, 3)>ab, 3c0, 0, 1
P4/nnc (126)<2; 3; 5 + (0, 0, 4); 9 + (0, 0, 5)>ab, 3c0, 0, 2

[p] c' = pc


P4/nnc (126)<2; 3; 5 + (0, 0, 2u); 9 + (0, 0, p/2 - 1/2 + 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p2] a' = pa, b' = pb


P4/nnc (126)<2 + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (2u, 0, 0); 9 + (p/2 - 1/2 + 2up/2 - 1/2 + 2v, 0)>papbcuv, 0
 prime p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups

[3] Pn-3n (222)

II Minimal non-isomorphic klassengleiche supergroups

[2] I4/mmm (139); [2] C4/mcc (124, P4/mcc)
[2] c' = 1/2c  P4/nbm (125)
P4/nnc No. 126 P4/n2/n2/c D4h4

ORIGIN CHOICE 2, Origin at -1 at n n (nc), at 1/41/41/4 from 4 2 2

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (9)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
16 k 1
(1) xyz(2) -x + 1/2-y + 1/2z(3) -y + 1/2xz(4) y-x + 1/2z
(5) -x + 1/2y-z + 1/2(6) x-y + 1/2-z + 1/2(7) yx-z + 1/2(8) -y + 1/2-x + 1/2-z + 1/2
(9) -x-y-z(10) x + 1/2y + 1/2-z(11) y + 1/2-x-z(12) -yx + 1/2-z
(13) x + 1/2-yz + 1/2(14) -xy + 1/2z + 1/2(15) -y-xz + 1/2(16) y + 1/2x + 1/2z + 1/2

I Maximal translationengleiche subgroups

[2] P-4n2 (118)1; 2; 7; 8; 11; 12; 13; 14 1/43/4, 0
[2] P-42c (112)1; 2; 5; 6; 11; 12; 15; 16 1/43/4, 0
[2] P4nc (104)1; 2; 3; 4; 13; 14; 15; 16 1/41/4, 0
[2] P422 (89)1; 2; 3; 4; 5; 6; 7; 8 1/41/41/4
[2] P4/n11 (85P4/n)1; 2; 3; 4; 9; 10; 11; 12
[2] P2/n12/c (68Ccce)1; 2; 7; 8; 9; 10; 15; 16a - ba + bc
[2] P2/n2/n1 (48Pnnn)1; 2; 5; 6; 9; 10; 13; 14

II Maximal klassengleiche subgroups

[3] c' = 3c

braceP4/nnc (126)<2; 3; 9; 5 + (0, 0, 1)>ab, 3c
P4/nnc (126)<2; 3; 5 + (0, 0, 3); 9 + (0, 0, 2)>ab, 3c0, 0, 1
P4/nnc (126)<2; 3; 5 + (0, 0, 5); 9 + (0, 0, 4)>ab, 3c0, 0, 2

[p] c' = pc


P4/nnc (126)<2; 3; 5 + (0, 0, p/2 - 1/2 + 2u); 9 + (0, 0, 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p2] a' = pa, b' = pb


P4/nnc (126)<2 + (p/2 - 1/2 + 2up/2 - 1/2 - 2v, 0); 3 + (p/2 - 1/2 + u + v, -u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 0); 9 + (2u, 2v, 0)>papbcuv, 0
 prime p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups

[3] Pn-3n (222)

II Minimal non-isomorphic klassengleiche supergroups

[2] I4/mmm (139); [2] C4/mcc (124, P4/mcc)
[2] c' = 1/2c  P4/nbm (125)








































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