Cmcm No. 63 C2/m2/c21/m D2h17

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

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 (0, 0, 0)+  (1/21/2, 0)+  
16 h 1
(1) xyz(2) -x-yz + 1/2(3) -xy-z + 1/2(4) x-y-z
(5) -x-y-z(6) xy-z + 1/2(7) x-yz + 1/2(8) -xyz

I Maximal translationengleiche subgroups

[2] C2cm (40Ama2)(1; 4; 6; 7)+cb, -a
[2] Cm2m (38Amm2)(1; 3; 6; 8)+cab 0, 0, 1/4
[2] Cmc21 (36)(1; 2; 7; 8)+
[2] C2221 (20)(1; 2; 3; 4)+
[2] C12/c1 (15)(1; 3; 5; 7)+
[2] C2/m11 (12C12/m1)(1; 4; 5; 8)+-bac
[2] C1121/m (11P1121/m)(1; 2; 5; 6)+1/2(a - b), 1/2(a + b), c

II Maximal klassengleiche subgroups

[2] Pbnm (62Pnma)1; 2; 5; 6; (3; 4; 7; 8) + (1/21/2, 0)bca
[2] Pmcn (62Pnma)1; 2; 7; 8; (3; 4; 5; 6) + (1/21/2, 0)cab1/41/4, 0
[2] Pbcn (60)1; 3; 5; 7; (2; 4; 6; 8) + (1/21/2, 0)
[2] Pmnm (59Pmmn)1; 3; 6; 8; (2; 4; 5; 7) + (1/21/2, 0)cab1/41/4, 0
[2] Pmnn (58Pnnm)1; 4; 5; 8; (2; 3; 6; 7) + (1/21/2, 0)bca
[2] Pbcm (57)1; 4; 6; 7; (2; 3; 5; 8) + (1/21/2, 0)1/41/4, 0
[2] Pbnn (52Pnna)1; 2; 3; 4; (5; 6; 7; 8) + (1/21/2, 0)bca1/41/4, 0
[2] Pmcm (51Pmma)1; 2; 3; 4; 5; 6; 7; 8cab

[3] a' = 3a

braceCmcm (63)<2; 3; 5>3abc
Cmcm (63)<(2; 3; 5) + (2, 0, 0)>3abc1, 0, 0
Cmcm (63)<(2; 3; 5) + (4, 0, 0)>3abc2, 0, 0

[3] b' = 3b

braceCmcm (63)<2; 3; 5>a, 3bc
Cmcm (63)<3; (2; 5) + (0, 2, 0)>a, 3bc0, 1, 0
Cmcm (63)<3; (2; 5) + (0, 4, 0)>a, 3bc0, 2, 0

[3] c' = 3c

braceCmcm (63)<5; (2; 3) + (0, 0, 1)>ab, 3c
Cmcm (63)<2 + (0, 0, 1); 3 + (0, 0, 3); 5 + (0, 0, 2)>ab, 3c0, 0, 1
Cmcm (63)<2 + (0, 0, 1); 3 + (0, 0, 5); 5 + (0, 0, 4)>ab, 3c0, 0, 2

[p] a' = pa


Cmcm (63)<(2; 3; 5) + (2u, 0, 0)>pabcu, 0, 0
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p] b' = pb


Cmcm (63)<3; (2; 5) + (0, 2u, 0)>apbc0, u, 0
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

[p] c' = pc


Cmcm (63)<2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/2 - 1/2 + 2u); 5 + (0, 0, 2u)>abpc0, 0, u
 prime p > 2; 0 ≤ u < p
p conjugate subgroups

I Minimal translationengleiche supergroups

[3] P63/mcm (193); [3] P63/mmc (194)

II Minimal non-isomorphic klassengleiche supergroups

[2] Fmmm (69)
[2] a' = 1/2a, b' = 1/2b  Pmcm (51, Pmma); [2] c' = 1/2c  Cmmm (65)








































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