P4/mbm No. 127 P4/m21/b2/m D4h5


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 8i 8j 8k 16l
I Maximal translationengleiche subgroups
[2] P-4b2 (117) 2a 2b 2d 2c 4e 4f 4g 4h 8i 8i 8i 2 × 8i
[2] P-421m(113) 2a 2b 2c 2c 4d 2 × 2c 4e 4e 8f 8f 2 × 4e 2 × 8f
[2] P4bm (100) 2a 2a 2b 2b 2 × 2a 2 × 2b 4c 4c 8d 8d 2 × 4c 2 × 8d
[2] P4212 (90) x + (1/2), y, z 2c 2c 2b 2a 2 × 2c 4d 4e 4f 8g 8g 8g 2 × 8g
[2] P4/m (83) 1a; 1c 1b; 1d 2f 2e 2g; 2h 4i 4j 4k 2 × 4j 2 × 4k 8l 2 × 8l
[2] Pbam (55) 2a 2b 2d 2c 4e 4f 4g 4h 2 × 4g 2 × 4h 8i 2 × 8i
[2] Cmmm(65) a - b, (1/2)(x - y) + (1/4), 4e 4f 2c; 2d 2a; 2b 8m 4k; 4l 4g; 4i 4h; 4j 2 × 8p 2 × 8q 8n; 8o 2 × 16r
a + b, c (1/2)(x + y) + (1/4), z
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P42/mnm a, b, 2c x + (1/2), y, (1/2)z; 4c 4d 4e 2a; 2b 8h 2 × 4e 4f; 4g 8j 2 × 8i 16k 2 × 8j 2 × 16k
(136) +(0, 0, (1/2))
[2] P42/mnm a, b, 2c x + (1/2), y, (1/2)z + (1/4); 4d 4c 2a; 2b 4e 8h 2 × 4e 8j 4f; 4g 16k 2 × 8i 2 × 8j 2 × 16k
(136) +(0, 0, (1/2))
[2] P42/mbc a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a 4b 4d 4c 8e 8f 8h 8g 2 × 8h 16i 16i 2 × 16i
(135)
[2] P42/mbc a, b, 2c x, y, (1/2)z + (1/4); 4b 4a 4c 4d 8e 8f 8g 8h 16i 2 × 8h 16i 2 × 16i
(135) +(0, 0, (1/2))
[2] P4/mnc a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2b 4e 4d 4c 2 × 4e 8f 8h 8g 2 × 8h 16i 16i 2 × 16i
(128)
[2] P4/mnc a, b, 2c x, y, (1/2)z + (1/4); 4e 2a; 2b 4c 4d 2 × 4e 8f 8g 8h 16i 2 × 8h 16i 2 × 16i
(128) +(0, 0, (1/2))
   Enlarged unit cell, isomorphic
[2] P4/mbm a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2b 4e 4f 2c; 2d 2 × 4e 2 × 4f 4g; 4h 8k 8i; 8j 16l 2 × 8k 2 × 16l
[2] P4/mbm a, b, 2c x, y, (1/2)z + (1/4); 4e 2a; 2b 2c; 2d 4f 2 × 4e 2 × 4f 8k 4g; 4h 16l 8i; 8j 2 × 8k 2 × 16l
+(0, 0, (1/2))
[3] P4/mbm a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4e 2b; 4e 2c; 4f 2d; 4f 3 × 4e 3 × 4f 4g; 8k 4h; 8k 8i; 16l 8j; 16l 3 × 8k 3 × 16l


Wyckoff positions
2a 2b 2c 2d 4e 4f
4g 4h 8i 8j 8k 16l
[p] P4/mbm a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 4e 2b; ((p - 1)/2) × 4e 2c; ((p - 1)/2) × 4f 2d; ((p - 1)/2) × 4f p × 4e p × 4f
p = prime > 2; 4g; ((p - 1)/2) × 8k 4h; ((p - 1)/2) × 8k 8i; ((p - 1)/2) × 16l 8j; ((p - 1)/2) × 16l p × 8k p × 16l
u = 1, . . ., p - 1
[9] P4/mbm 3a, 3b, c (1/3)x, (1/3)y, z; 2a; 2 × 8i 2b; 2 × 8j 2c; 2 × 4h; 8j 2d; 2 × 4g; 8i 4e; 2 × 16l 4f; 2 × 8k; 16l
±((1/3), 0, 0); ±(0, (1/3), 0); 3 × 4g; 3 × 8i 3 × 4h; 3 × 8j 9 × 8i 9 × 8j 3 × 8k; 3 × 16l 9 × 16l
±((1/3), (1/3), 0); ±((1/3), (2/3), 0)
[p2] P4/mbm pa, pb, c (1/p)x, (1/p)y, z; 2a; ((p2 - 1)/4) × 8i 2b; ((p2 - 1)/4) × 8j 2c; (p - 1) × 4h; 2d; (p - 1) × 4g; 4e; ((p2 - 1)/4) × 16l 4f; (p - 1) × 8k;
+((u/p), (v/p), 0) (((p - 1)2)/4) × 8j (((p - 1)2)/4) × 8i (((p - 1)2)/4) × 16l
p = prime > 2; p × 4g; p × 4h; p2 × 8i p2 × 8j p × 8k; p2 × 16l
u, v = 1, . . ., p - 1 ((p(p - 1))/2) × 8i ((p(p - 1))/2) × 8j ((p(p - 1))/2) × 16l









































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