P4/mcc No. 124 P4/m2/c2/c D4h2


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 8i 8j 8k
8l 8m 16n
I Maximal translationengleiche subgroups
[2] P-4c2 (116) 2a 2c 2b 2d 4i 4i 4g 4h 2 × 4i 4e; 4f 8j
8j 8j 2 × 8j
[2] P-42c (112) 2a 2e 2c 2f 4m 2b; 2d 4k 4l 2 × 4m 8n 4g; 4j
4h; 4i 8n 2 × 8n
[2] P4cc (103) 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 2 × 4c 8d 8d
8d 8d 2 × 8d
[2] P422 (89) x, y, z + (1/4) 1a; 1b 2g 1c; 1d 2h 4i 2e; 2f 2 × 2g 2 × 2h 2 × 4i 4j; 4k 4l; 4n
4m; 4o 8p 2 × 8p
[2] P4/m (83) 2g 1a; 1b 2h 1c; 1d 2e; 2f 4i 2 × 2g 2 × 2h 2 × 4i 8l 8l
8l 4j; 4k 2 × 8l
[2] Pccm (49) 2e 2a 2h 2b 2c; 2d 2f; 2g 4m 4n 4o; 4p 8r 4i; 4k
4j; 4l 2 × 4q 2 × 8r
[2] Cccm (66) a - b, (1/2)(x - y), (1/2)(x + y), z 4a 4c 4b 4d 4e; 4f 8k 8i 8j 2 × 8k 8g; 8h 16m
a + b, c 16m 2 × 8l 2 × 16m
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P4/ncc a - b, origin 1 : (1/2)(x - y), 4a 4b 4c 4c 8d 8f 8e 2 × 4c 16g 16g 2 × 8f
(130) a + b, c (1/2)(x + y), z; +((1/2), (1/2), 0) 16g 16g 2 × 16g
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P4/ncc a - b, origin 1 : (1/2)(x - y) + (1/2), 4c 4c 4a 4b 8d 8f 2 × 4c 8e 16g 16g 16g
(130) a + b, c (1/2)(x + y), z; +((1/2), (1/2), 0) 2 × 8f 16g 2 × 16g
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P4/mnc a - b, (1/2)(x - y), (1/2)(x + y), z; 4e 2a; 2b 4d 4c 8h 8g 2 × 4e 8f 16i 16i 16i
(128) a + b, c +((1/2), (1/2), 0) 2 × 8g 2 × 8h 2 × 16i
[2] P4/mnc a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), z; 4d 4c 4e 2a; 2b 8h 8g 8f 2 × 4e 16i 16i 2 × 8g
(128) a + b, c +((1/2), (1/2), 0) 16i 2 × 8h 2 × 16i
[2] P4/nnc a - b, origin 1 : (1/2)(x - y), 2a; 2b 4e 4c 4d 8f 8h 2 × 4e 8g 16k 8i; 8j 2 × 8h
(126) a + b, c (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 16k 16k 2 × 16k
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P4/nnc a - b, origin 1 : (1/2)(x - y) + (1/2), 4c 4d 2a; 2b 4e 8f 8h 8g 2 × 4e 16k 8i; 8j 16k
(126) a + b, c (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 2 × 8h 16k 2 × 16k
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)


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









































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