P42/nmc No. 137 P42/n21/m2/c D4h15

ORIGIN CHOICE 1, Origin at -4m 2/n, at -1/41/4, -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 h 1
(1) xyz(2) -x-yz(3) -y + 1/2x + 1/2z + 1/2(4) y + 1/2-x + 1/2z + 1/2
(5) -x + 1/2y + 1/2-z + 1/2(6) x + 1/2-y + 1/2-z + 1/2(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-x-z(12) -yx-z
(13) x-yz(14) -xyz(15) -y + 1/2-x + 1/2z + 1/2(16) y + 1/2x + 1/2z + 1/2

I Maximal translationengleiche subgroups

[2] P-4m2 (115)1; 2; 7; 8; 11; 12; 13; 14
[2] P-421c (114)1; 2; 5; 6; 11; 12; 15; 16
[2] P42mc (105)1; 2; 3; 4; 13; 14; 15; 16 0, 1/2, 0
[2] P42212 (94)1; 2; 3; 4; 5; 6; 7; 8
[2] P42/n11 (86P42/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/n21/m1 (59Pmmn)1; 2; 5; 6; 9; 10; 13; 14 0, 0, 1/4

II Maximal klassengleiche subgroups

[3] c' = 3c

braceP42/nmc (137)<2; (3; 5; 9) + (0, 0, 1)>ab, 3c
P42/nmc (137)<2; 3 + (0, 0, 1); (5; 9) + (0, 0, 3)>ab, 3c0, 0, 1
P42/nmc (137)<2; 3 + (0, 0, 1); (5; 9) + (0, 0, 5)>ab, 3c0, 0, 2

[p] c' = pc


P42/nmc (137)<2; 3 + (0, 0, p/2 - 1/2); (5; 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


P42/nmc (137)<2 + (2u, 2v, 0); 3 + (p/2 - 1/2 + u + vp/2 - 1/2 - u + v, 0); 5 + (p/2 - 1/2 + 2up/2 - 1/2, 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

none

II Minimal non-isomorphic klassengleiche supergroups

[2] C42/mmc (132, P42/mcm); [2] I4/mmm (139)
[2] c' = 1/2c  P4/nmm (129)
P42/nmc No. 137 P42/n21/m2/c D4h15

ORIGIN CHOICE 2, Origin at -1 at n 21 (cn), at 1/4, -1/41/4 from -4 m 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 h 1
(1) xyz(2) -x + 1/2-y + 1/2z(3) -y + 1/2xz + 1/2(4) y-x + 1/2z + 1/2
(5) -xy + 1/2-z(6) x + 1/2-y-z(7) y + 1/2x + 1/2-z + 1/2(8) -y-x-z + 1/2
(9) -x-y-z(10) x + 1/2y + 1/2-z(11) y + 1/2-x-z + 1/2(12) -yx + 1/2-z + 1/2
(13) x-y + 1/2z(14) -x + 1/2yz(15) -y + 1/2-x + 1/2z + 1/2(16) yxz + 1/2

I Maximal translationengleiche subgroups

[2] P-4m2 (115)1; 2; 7; 8; 11; 12; 13; 14 1/43/41/4
[2] P-421c (114)1; 2; 5; 6; 11; 12; 15; 16 1/43/41/4
[2] P42mc (105)1; 2; 3; 4; 13; 14; 15; 16 1/41/4, 0
[2] P42212 (94)1; 2; 3; 4; 5; 6; 7; 8 1/43/41/4
[2] P42/n11 (86P42/n)1; 2; 3; 4; 9; 10; 11; 12 0, 1/2, 0
[2] P2/n12/c (68Ccce)1; 2; 7; 8; 9; 10; 15; 16a - ba + bc 0, 1/2, 0
[2] P2/n21/m1 (59Pmmn)1; 2; 5; 6; 9; 10; 13; 14

II Maximal klassengleiche subgroups

[3] c' = 3c

braceP42/nmc (137)<2; 5; 9; 3 + (0, 0, 1)>ab, 3c
P42/nmc (137)<2; 3 + (0, 0, 1); (5; 9) + (0, 0, 2)>ab, 3c0, 0, 1
P42/nmc (137)<2; 3 + (0, 0, 1); (5; 9) + (0, 0, 4)>ab, 3c0, 0, 2

[p] c' = pc


P42/nmc (137)<2; 3 + (0, 0, p/2 - 1/2); (5; 9) + (0, 0, 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p2] a' = pa, b' = pb


P42/nmc (137)<2 + (p/2 - 1/2 + 2up/2 - 1/2 + 2v, 0); 3 + (p/2 - 1/2 + u + v, -u + v, 0); 5 + (2up/2 - 1/2, 0); 9 + (2u, 2v, 0)>papbcuv, 0
 prime p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups

none

II Minimal non-isomorphic klassengleiche supergroups

[2] C42/mmc (132, P42/mcm); [2] I4/mmm (139)
[2] c' = 1/2c  P4/nmm (129)








































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