I4/mmm No. 139 I4/m2/m2/m D4h17

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/21/2); (2); (3); (5); (9)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 (0, 0, 0)+  (1/21/21/2)+  
32 o 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-y-z(10) xy-z(11) y-x-z(12) -yx-z
(13) x-yz(14) -xyz(15) -y-xz(16) yxz

I Maximal translationengleiche subgroups

[2] I-42m (121)(1; 2; 5; 6; 11; 12; 15; 16)+
[2] I-4m2 (119)(1; 2; 7; 8; 11; 12; 13; 14)+
[2] I4mm (107)(1; 2; 3; 4; 13; 14; 15; 16)+
[2] I422 (97)(1; 2; 3; 4; 5; 6; 7; 8)+
[2] I4/m11 (87I4/m)(1; 2; 3; 4; 9; 10; 11; 12)+
[2] I2/m2/m1 (71Immm)(1; 2; 5; 6; 9; 10; 13; 14)+
[2] I2/m12/m (69Fmmm)(1; 2; 7; 8; 9; 10; 15; 16)+a - ba + bc

II Maximal klassengleiche subgroups

[2] P42/nmc (137)1; 2; 7; 8; 11; 12; 13; 14; (3; 4; 5; 6; 9; 10; 15; 16) + (1/21/21/2)1/43/41/4
[2] P42/mnm (136)1; 2; 7; 8; 9; 10; 15; 16; (3; 4; 5; 6; 11; 12; 13; 14) + (1/21/21/2)
[2] P42/nnm (134)1; 2; 5; 6; 11; 12; 15; 16; (3; 4; 7; 8; 9; 10; 13; 14) + (1/21/21/2)1/43/41/4
[2] P42/mmc (131)1; 2; 5; 6; 9; 10; 13; 14; (3; 4; 7; 8; 11; 12; 15; 16) + (1/21/21/2)0, 1/2, 0
[2] P4/nmm (129)1; 2; 3; 4; 13; 14; 15; 16; (5; 6; 7; 8; 9; 10; 11; 12) + (1/21/21/2)1/41/41/4
[2] P4/mnc (128)1; 2; 3; 4; 9; 10; 11; 12; (5; 6; 7; 8; 13; 14; 15; 16) + (1/21/21/2)
[2] P4/nnc (126)1; 2; 3; 4; 5; 6; 7; 8; (9; 10; 11; 12; 13; 14; 15; 16) + (1/21/21/2)1/41/41/4
[2] P4/mmm (123)1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16

[3] c' = 3c

braceI4/mmm (139)<2; 3; 5; 9>ab, 3c
I4/mmm (139)<2; 3; (5; 9) + (0, 0, 2)>ab, 3c0, 0, 1
I4/mmm (139)<2; 3; (5; 9) + (0, 0, 4)>ab, 3c0, 0, 2

[p] c' = pc


I4/mmm (139)<2; 3; (5; 9) + (0, 0, 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p2] a' = pa, b' = pb


I4/mmm (139)<(2; 9) + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (2u, 0, 0)>papbcuv, 0
 prime p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups

[3] Fm-3m (225); [3] Im-3m (229)

II Minimal non-isomorphic klassengleiche supergroups

none
[2] c' = 1/2c  C4/mmm (123, P4/mmm)








































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