P-6m2 No. 187 D3h1


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 1e 1f 2g 2h 2i 3j 3k
6l 6m 6n 12o
I Maximal translationengleiche subgroups
[2] P-6 (174) 1a 1b 1c 1d 1e 1f 2g 2h 2i 3j 3k
2 × 3j 2 × 3k 6l 2 × 6l
[2] P3m1 1a 1a 1b 1b 1c 1c 2 × 1a 2 × 1b 2 × 1c 3d 3d
  (156) 6e 6e 2 × 3d 2 × 6e
[2] P312 1a 1b 1c 1d 1e 1f 2g 2h 2i 3j 3k
  (149) 6l 6l 6l 2 × 6l
[3] Cm2m a, a + 2b, c x - (1/2)y, (1/2)y, z 2a 2b 2a 2b 2a 2b 4c 4c 4c 2a; 4d 2b; 4e
  (38) 3 × 4d 3 × 4e 4c; 8f 3 × 8f
 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]Amm2 c, a, a + 2b z, x - (1/2)y, (1/2)y
  or 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)
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P-6c2 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2b 2c 2d 2e 2f 4g 4h 4i 6j 6k
  (188) 12l 2 × 6k 12l 2 × 12l
[2] P-6c2 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2b 2a 2d 2c 2f 2e 4g 4h 4i 6k 6j
  (188) 2 × 6k 12l 12l 2 × 12l
[3] P-62m 2a + b, (1/3)(x + y), (1/3)(-x + 2y), z; 1a; 2c 1b; 2d 3f 3g 3f 3g 2e; 4h 6i 6i 3f; 6j 3g; 6k
  (189) -a + b, c ±((1/3), (2/3), 0) 3 × 6j 3 × 6k 6i; 12l 3 × 12l
[3] P-62m 2a + b, (1/3)(x + y) + (1/3), (1/3)(-x + 2y), z; 3f 3g 1a; 2c 1b; 2d 3f 3g 6i 2e; 4h 6i 3f; 6j 3g; 6k
  (189) -a + b, c ±((1/3), (2/3), 0) 3 × 6j 3 × 6k 6i; 12l 3 × 12l
[3] P-62m 2a + b, (1/3)(x + y) - (1/3), (1/3)(-x + 2y), z; 3f 3g 3f 3g 1a; 2c 1b; 2d 6i 6i 2e; 4h 3f; 6j 3g; 6k
  (189) -a + b, c ±((1/3), (2/3), 0) 3 × 6j 3 × 6k 6i; 12l 3 × 12l
   Enlarged unit cell, isomorphic
[2] P-6m2 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 1a; 1b 2g 1c; 1d 2h 1e; 1f 2i 2 × 2g 2 × 2h 2 × 2i 3j; 3k 6n
6l; 6m 12o 2 × 6n 2 × 12o
[2] P-6m2 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2g 1a; 1b 2h 1c; 1d 2i 1e; 1f 2 × 2g 2 × 2h 2 × 2i 6n 3j; 3k
12o 6l; 6m 2 × 6n 2 × 12o
[3] P-6m2 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 1a; 2g 1b; 2g 1c; 2h 1d; 2h 1e; 2i 1f; 2i 3 × 2g 3 × 2h 3 × 2i 3j; 6n 3k; 6n
6l; 12o 6m; 12o 3 × 6n 3 × 12o


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 1e 1f 2g
2h 2i 3j 3k 6l
6m 6n 12o
[p] P-6m2 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 1a; ((p - 1)/2) × 2g 1b; ((p - 1)/2) × 2g 1c; ((p - 1)/2) × 2h 1d; ((p - 1)/2) × 2h 1e; ((p - 1)/2) × 2i 1f; ((p - 1)/2) × 2i p × 2g
p = prime > 2; p × 2h p × 2i 3j; ((p - 1)/2) × 6n 3k; ((p - 1)/2) × 6n 6l; ((p - 1)/2) × 12o
u = 1, . . ., p - 1 6m; ((p - 1)/2) × 12o p × 6n p × 12o
[4] P-6m2 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 1a; 3j 1b; 3k 1e; 3j 1f; 3k 1c; 3j 1d; 3k 2g; 6n
+(0, (1/2), 0); +((1/2), (1/2), 0) 2i; 6n 2h; 6n 2 × 3j; 6l 2 × 3k; 6m 4 × 6l
4 × 6m 2 × 6n; 12o 4 × 12o
[p2] P-6m2 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; 1b; 1c(e*); 1d(f*); 1e(c*); 1f(d*); 2g;
p = prime ≠ 3; (p - 1) × 3j; (p - 1) × 3k; (p - 1) × 3j; (p - 1) × 3k; (p - 1) × 3j; (p - 1) × 3k; (p - 1) × 6n;
u, v = 1, . . ., p - 1 (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) ×
6l 6m 6l 6m 6l 6m 12o
2h(i*); 2i(h*); p × 3j; p × 3k; p2 × 6l
(p - 1) × 6n; (p - 1) × 6n; ((p(p - 1))/2) × 6l ((p(p - 1))/2) × 6m
(((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) ×
12o 12o
p2 × 6m p × 6n; p2 × 12o
((p(p - 1))/2) × 12o
* p = 3n - 1









































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