P-6c2 No. 188 D3h2


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f
4g 4h 4i 6j 6k 12l
I Maximal translationengleiche subgroups
[2] P-6 (174) x, y, z + (1/4) 2g 1a; 1b 2h 1c; 1d 2i 1e; 1f
2 × 2g 2 × 2h 2 × 2i 6l 3j; 3k 2 × 6l
[2] P3c1 2a 2a 2b 2b 2c 2c
  (158) 2 × 2a 2 × 2b 2 × 2c 6d 6d 2 × 6d
[2] P312 1a; 1b 2g 1c; 1d 2h 1e; 1f 2i
  (149) 2 × 2g 2 × 2h 2 × 2i 3j; 3k 6l 2 × 6l
[3] C2cm 2a+b, b, c (1/2)x, -(1/2)x + y, z 4a 4b 4a 4b 4a 4b
  (40) 8c 8c 8c 4a; 8c 3 × 4b 3 × 8c
 conjugate: -a + b, -a - b, c (1/2)(-x + y), (1/2)(-x - y), z
 conjugate: -a - 2b, a, c -(1/2)y, x - (1/2)y, z
[conventional setting]Ama2 c, -b, 2a + b z, (1/2)x - y, (1/2)x
  or c, a + b, -a + b z, (1/2)(x + y), (1/2)(-x + y)
  or c, -a, -a - 2b z, -x + (1/2)y, -(1/2)y
 alternative:
Cc2m a, a + 2b, c x - (1/2)y, (1/2)y, z
  or b, -2a - b, c -(1/2)x + y, -(1/2)x, z
  or -a - b, a - b, c -(1/2)(x + y), (1/2)(x - y), z
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[3] P-62c a - b, (1/3)(2x - y), (1/3)(x + y), z; 2a; 4f 2b; 2c; 2d 6g 6h 6g 6h
  (190) a + 2b, c ±((1/3), (2/3), 0) 4e; 2 × 4f 12i 12i 6g; 12i 3 × 6h 3 × 12i
[3] P-62c a - b, (1/3)(2x - y) + (1/3), (1/3)(x + y), z; 6g 6h 6g 6h 2a; 4f 2b; 2c; 2d
  (190) a + 2b, c ±((1/3), (2/3), 0) 12i 12i 4e; 2 × 4f 6g; 12i 3 × 6h 3 × 12i
[3] P-62c a - b, (1/3)(2x - y) - (1/3), (1/3)(x + y), z; 6g 6h 2a; 4f 2b; 2c; 2d 6g 6h
  (190) a + 2b, c ±((1/3), (2/3), 0) 12i 4e; 2 × 4f 12i 6g; 12i 3 × 6h 3 × 12i
   Enlarged unit cell, isomorphic
[3] P-6c2 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4h 2d; 4h 2e; 4i 2f; 4i
3 × 4g 3 × 4h 3 × 4i 6j; 12l 6k; 12l 3 × 12l
[p] P-6c2 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 4g 2b; ((p - 1)/2) × 4g 2c; ((p - 1)/2) × 4h 2d; ((p - 1)/2) × 4h 2e; ((p - 1)/2) × 4i 2f; ((p - 1)/2) × 4i
p = prime > 2; u = 1, . . ., p - 1 p × 4g p × 4h p × 4i 6j; ((p - 1)/2) × 12l 6k; ((p - 1)/2) × 12l p × 12l
[4] P-6c2 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 2a; 6j 2b; 6k 2e; 6j 2f; 6k 2c; 6j 2d; 6k
+(0, (1/2), 0); +((1/2), (1/2), 0) 4g; 12l 4i; 12l 4h; 12l 2 × 6j; 12l 4 × 6k 4 × 12l
[p2] P-6c2 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 2a; (p - 1) × 6j; 2b; ((p2 - 1)/3) × 6k 2c(e*); 2d(f*); 2e(c*); 2f(d*);
p = prime ≠ 3; u, v = 1, . . ., p - 1 (((p - 1)(p - 2))/6) × 12l (p - 1) × 6j; ((p2 - 1)/3) × 6k (p - 1) × 6j; ((p2 - 1)/3) × 6k
(((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) ×
12l 12l
4g; ((p2 - 1)/3) × 12l 4h(i*); 4i(h*); p × 6j p2 × 6k p2 × 12l
((p2 - 1)/3) × 12l ((p2 - 1)/3) × 12l ((p(p - 1))/2) × 12l
* p = 3n - 1









































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