P42cm No. 101 P42cm C4v3

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
8 e 1
(1) xyz(2) -x-yz(3) -yxz + 1/2(4) y-xz + 1/2
(5) x-yz + 1/2(6) -xyz + 1/2(7) -y-xz(8) yxz

I Maximal translationengleiche subgroups

[2] P4211 (77P42)1; 2; 3; 4
[2] P21m (35Cmm2)1; 2; 7; 8a - ba + bc
[2] P2c1 (27Pcc2)1; 2; 5; 6

II Maximal klassengleiche subgroups

[2] a' = 2a, b' = 2b

C42cd (106, P42bc)<2; 3; 5 + (0, 1, 0)>a - ba + bc
C42cd (106, P42bc)<2; 5; 3 + (1, 0, 0)>a - ba + bc1/21/2, 0
C42cm (105, P42mc)<2; 3; 5>a - ba + bc
C42cm (105, P42mc)<2; 3 + (1, 0, 0); 5 + (0, 1, 0)>a - ba + bc1/21/2, 0

[3] c' = 3c

P42cm (101)<2; (3; 5) + (0, 0, 1)>ab, 3c

[p] c' = pc


P42cm (101)<2; (3; 5) + (0, 0, p/2 - 1/2)>abpc
 prime p > 2
no conjugate subgroups

[p2] a' = pa, b' = pb


P42cm (101)<2 + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (0, 2v, 0)>papbcuv, 0
 prime p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups

I Minimal translationengleiche supergroups

[2] P42/mcm (132); [2] P42/ncm (138)

II Minimal non-isomorphic klassengleiche supergroups

[2] C42cm (105, P42mc); [2] I4cm (108)
[2] c' = 1/2c  P4mm (99)








































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