P4/nmm No. 129 P4/n21/m2/m D4h7

ORIGIN CHOICE 1, Origin at -4m 2 at -4/n m 2/g, at -1/41/4, 0 from centre (2/m)

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

I Maximal translationengleiche subgroups

[2] P-4m2 (115)1; 2; 7; 8; 11; 12; 13; 14
[2] P-421m (113)1; 2; 5; 6; 11; 12; 15; 16
[2] P4mm (99)1; 2; 3; 4; 13; 14; 15; 16 1/2, 0, 0
[2] P4212 (90)1; 2; 3; 4; 5; 6; 7; 8
[2] P4/n11 (85P4/n)1; 2; 3; 4; 9; 10; 11; 12
[2] P2/n12/m (67Cmme)1; 2; 7; 8; 9; 10; 15; 16a - ba + bc 1/43/4, 0
[2] P2/n21/m1 (59Pmmn)1; 2; 5; 6; 9; 10; 13; 14

II Maximal klassengleiche subgroups

[2] c' = 2c

P42/ncm (138)<2; 9; (3; 5) + (0, 0, 1)>ab, 2c0, 0, -1/2
P42/ncm (138)<2; 5; (3; 9) + (0, 0, 1)>ab, 2c
P42/nmc (137)<2; 5; 9; 3 + (0, 0, 1)>ab, 2c0, 0, -1/2
P42/nmc (137)<2; (3; 5; 9) + (0, 0, 1)>ab, 2c
P4/ncc (130)<2; 3; 9; 5 + (0, 0, 1)>ab, 2c
P4/ncc (130)<2; 3; 5; 9 + (0, 0, 1)>ab, 2c0, 0, 1/2
P4/nmm (129)<2; 3; 5; 9>ab, 2c
P4/nmm (129)<2; 3; (5; 9) + (0, 0, 1)>ab, 2c0, 0, 1/2

[3] c' = 3c

braceP4/nmm (129)<2; 3; 5; 9>ab, 3c
P4/nmm (129)<2; 3; (5; 9) + (0, 0, 2)>ab, 3c0, 0, 1
P4/nmm (129)<2; 3; (5; 9) + (0, 0, 4)>ab, 3c0, 0, 2

[p] c' = pc


P4/nmm (129)<2; 3; (5; 9) + (0, 0, 2u)>abpc0, 0, u
 p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p

[p2] a' = pa, b' = pb


P4/nmm (129)<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
 p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p

I Minimal translationengleiche supergroups

none

II Minimal non-isomorphic klassengleiche supergroups

[2] C4/mmm (123, P4/mmm); [2] I4/mmm (139)
none








































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