Pmn21 No. 31 Pmn21 C2v7

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 
4 b 1
(1) xyz(2) -x + 1/2-yz + 1/2(3) x + 1/2-yz + 1/2(4) -xyz

I Maximal translationengleiche subgroups

[2] P1n1 (7P1c1)1; 3cb, -a - c
[2] Pm11 (6P1m1)1; 4cab
[2] P1121 (4)1; 2 1/4, 0, 0

II Maximal klassengleiche subgroups

[2] b' = 2b

Pbn21 (33, Pna21)<2; 3 + (0, 1, 0)>-2bac1/4, 0, 0
Pbn21 (33, Pna21)<3; 2 + (0, 1, 0)>-2bac1/41/2, 0
Pmn21 (31)<2; 3>a, 2bc
Pmn21 (31)<(2; 3) + (0, 1, 0)>a, 2bc0, 1/2, 0

[3] a' = 3a

bracePmn21 (31)<(2; 3) + (1, 0, 0)>3abc
Pmn21 (31)<2 + (3, 0, 0); 3 + (1, 0, 0)>3abc1, 0, 0
Pmn21 (31)<2 + (5, 0, 0); 3 + (1, 0, 0)>3abc2, 0, 0

[3] b' = 3b

bracePmn21 (31)<2; 3>a, 3bc
Pmn21 (31)<(2; 3) + (0, 2, 0)>a, 3bc0, 1, 0
Pmn21 (31)<(2; 3) + (0, 4, 0)>a, 3bc0, 2, 0

[3] c' = 3c

Pmn21 (31)<(2; 3) + (0, 0, 1)>ab, 3c

[p] a' = pa


Pmn21 (31)<2 + (p/2 - 1/2 + 2u, 0, 0); 3 + (p/2 - 1/2, 0, 0)>pabcu, 0, 0
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p] b' = pb


Pmn21 (31)<(2; 3) + (0, 2u, 0)>apbc0, u, 0
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p] c' = pc


Pmn21 (31)<(2; 3) + (0, 0, p/2 - 1/2)>abpc
 prime p > 2
no conjugate subgroups

I Minimal translationengleiche supergroups

[2] Pmna (53); [2] Pnnm (58); [2] Pmmn (59); [2] Pnma (62)

II Minimal non-isomorphic klassengleiche supergroups

[2] Cmc21 (36); [2] Bmm2 (38, Amm2); [2] Ama2 (40); [2] Imm2 (44)
[2] a' = 1/2a  Pmc21 (26); [2] c' = 1/2c  Pma2 (28)








































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