P-62c No. 190 D3h4


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f
6g 6h 12i
I Maximal translationengleiche subgroups
[2] P-6 (174) x, y, z + (1/4) 2g 1a; 1b 1d; 1e 1c; 1f 2 × 2g 2h; 2i
6l 3j; 3k 2 × 6l
[2] P31c 2a 2a 2b 2b 2 × 2a 2 × 2b
  (159) 6c 6c 2 × 6c
[2] P321 1a; 1b 2c 2d 2d 2 × 2c 2 × 2d
  (150) 3e; 3f 6g 2 × 6g
[3] C2cm a, a + 2b, c x - (1/2)y, (1/2)y, z 4a 4b 4b 4b 8c 8c
  (40) 4a; 8c 3 × 4b 3 × 8c
 conjugate: b, -2a - b, c -(1/2)x + y, -(1/2)x, z
 conjugate: -a - b, a - b, c -(1/2)(x + y), (1/2)(x - y), z
[conventional setting]Ama2 c, a + 2b, -a z, (1/2)y, -x + (1/2)y
  or c, -2a - b, -b z, -(1/2)x, (1/2)x - y
  or c, a - b, a + b z, (1/2)(x - y), (1/2)(x + y)
 alternative:
Cc2m 2a + b, b, c (1/2)x, -(1/2)x + y, z
  or -a - 2b, a, c -(1/2)y, x - (1/2)y, 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-6c2 2a + b, -a + b, c (1/3)(x + y), (1/3)(-x + 2y), z; 2a; 2c; 2e 2b; 2d; 2f 6k 6k 4g; 4h; 4i 12l
  (188) ±((1/3), (2/3), 0) 3 × 6j 3 × 6k 3 × 12l
   Enlarged unit cell, isomorphic
[3] P-62c a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4e 2b; 4e 2d; 4f 2c; 4f 3 × 4e 3 × 4f
6g; 12i 6h; 12i 3 × 12i
[p] P-62c a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 4e 2b; ((p - 1)/2) × 4e 2c(d*); 2d(c*); p × 4e p × 4f
p = prime > 2; u = 1, . . ., p - 1 ((p - 1)/2) × 4f ((p - 1)/2) × 4f
6g; ((p - 1)/2) × 12i 6h; ((p - 1)/2) × 12i p × 12i
[4] P-62c 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 2a; 6g 2b; 6h 2d; 6h 2c; 6h 4e; 12i 4 f; 12i
+(0, (1/2), 0); +((1/2), (1/2), 0) 2 × 6g; 12i 4 × 6h 4 × 12i
[p2] P-62c pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 2a; (p - 1) × 6g; 2b; ((p2 - 1)/3) × 6h 2c(d† ); 2d(c† ); 4e; ((p2 - 1)/3) × 12i 4f; ((p2 - 1)/3) ×
12i
p = prime ≠ 3; u, v = 1, . . ., p - 1 (((p - 1)(p - 2))/6) × 12i ((p2 - 1)/3) × 6h ((p2 - 1)/3) × 6h
p × 6g; p2 × 6h p2 × 12i
((p(p - 1))/2) × 12i
* p = 4n - 1 † p = 3n - 1









































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