P2/m C2h1 2/m Monoclinic No. 10 P12/m1 Patterson symmetry P12/m1 UNIQUE AXIS b

Origin at centre (2/m)

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1

Symmetry operations

 (1)  1 (2)  2   0, y, 0 (3)  -1   0, 0, 0 (4)  m   x, 0, z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 o 1
 (1) x, y, z (2) -x, y, -z (3) -x, -y, -z (4) x, -y, z
no conditions
Special: as above, plus
 2 n m
 x, 1/2, z -x, 1/2, -z
no extra conditions
 2 m m
 x, 0, z -x, 0, -z
no extra conditions
 2 l 2
 1/2, y, 1/2 1/2, -y, 1/2
no extra conditions
 2 k 2
 0, y, 1/2 0, -y, 1/2
no extra conditions
 2 j 2
 1/2, y, 0 1/2, -y, 0
no extra conditions
 2 i 2
 0, y, 0 0, -y, 0
no extra conditions
 1 h 2/m
 1/2, 1/2, 1/2
no extra conditions
 1 g 2/m
 1/2, 0, 1/2
no extra conditions
 1 f 2/m
 0, 1/2, 1/2
no extra conditions
 1 e 2/m
 1/2, 1/2, 0
no extra conditions
 1 d 2/m
 1/2, 0, 0
no extra conditions
 1 c 2/m
 0, 0, 1/2
no extra conditions
 1 b 2/m
 0, 1/2, 0
no extra conditions
 1 a 2/m
 0, 0, 0
no extra conditions

Symmetry of special projections

 Along [001]   p2mma' = ap   b' = b   Origin at 0, 0, z Along [100]   p2mma' = b   b' = cp   Origin at x, 0, 0 Along [010]   p2a' = c   b' = a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1m1 (Pm, 6) 1; 4 [2] P121 (P2, 3) 1; 2 [2] P-1 (2) 1; 3
 IIa none
 IIb [2] P121/m1 (b' = 2b) (P21/m, 11); [2] P12/c1 (c' = 2c) (P2/c, 13); [2] P12/a1 (a' = 2a) (P2/c, 13); [2] B12/e1 (a' = 2a, c' = 2c) (P2/c, 13); [2] C12/m1 (a' = 2a, b' = 2b) (C2/m, 12); [2] A12/m1 (b' = 2b, c' = 2c) (C2/m, 12); [2] F12/m1 (a' = 2a, b' = 2b, c' = 2c) (C2/m, 12)

Maximal isomorphic subgroups of lowest index

 IIc [2] P12/m1 (b' = 2b) (P2/m, 10); [2] P12/m1 (c' = 2c or a' = 2a or a' = a + c, c' = -a + c) (P2/m, 10)

Minimal non-isomorphic supergroups

 I [2] Pmmm (47); [2] Pccm (49); [2] Pmma (51); [2] Pmna (53); [2] Pbam (55); [2] Pnnm (58); [2] Cmmm (65); [2] Cccm (66); [2] P4/m (83); [2] P42/m (84); [3] P6/m (175)
 II [2] C12/m1 (C2/m, 12); [2] A12/m1 (C2/m, 12); [2] I12/m1 (C2/m, 12)

 P2/m C2h1 2/m Monoclinic No. 10 P112/m Patterson symmetry P112/m UNIQUE AXIS c

Origin at centre (2/m)

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2

Symmetry operations

 (1)  1 (2)  2   0, 0, z (3)  -1   0, 0, 0 (4)  m   x, y, 0

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 o 1
 (1) x, y, z (2) -x, -y, z (3) -x, -y, -z (4) x, y, -z
no conditions
Special: as above, plus
 2 n m
 x, y, 1/2 -x, -y, 1/2
no extra conditions
 2 m m
 x, y, 0 -x, -y, 0
no extra conditions
 2 l 2
 1/2, 1/2, z 1/2, 1/2, -z
no extra conditions
 2 k 2
 1/2, 0, z 1/2, 0, -z
no extra conditions
 2 j 2
 0, 1/2, z 0, 1/2, -z
no extra conditions
 2 i 2
 0, 0, z 0, 0, -z
no extra conditions
 1 h 2/m
 1/2, 1/2, 1/2
no extra conditions
 1 g 2/m
 1/2, 1/2, 0
no extra conditions
 1 f 2/m
 1/2, 0, 1/2
no extra conditions
 1 e 2/m
 0, 1/2, 1/2
no extra conditions
 1 d 2/m
 0, 1/2, 0
no extra conditions
 1 c 2/m
 1/2, 0, 0
no extra conditions
 1 b 2/m
 0, 0, 1/2
no extra conditions
 1 a 2/m
 0, 0, 0
no extra conditions

Symmetry of special projections

 Along [001]   p2a' = a   b' = b   Origin at 0, 0, z Along [100]   p2mma' = bp   b' = c   Origin at x, 0, 0 Along [010]   p2mma' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P11m (Pm, 6) 1; 4 [2] P112 (P2, 3) 1; 2 [2] P-1 (2) 1; 3
 IIa none
 IIb [2] P1121/m (c' = 2c) (P21/m, 11); [2] P112/a (a' = 2a) (P2/c, 13); [2] P112/b (b' = 2b) (P2/c, 13); [2] C112/e (a' = 2a, b' = 2b) (P2/c, 13); [2] A112/m (b' = 2b, c' = 2c) (C2/m, 12); [2] B112/m (a' = 2a, c' = 2c) (C2/m, 12); [2] F112/m (a' = 2a, b' = 2b, c' = 2c) (C2/m, 12)

Maximal isomorphic subgroups of lowest index

 IIc [2] P112/m (c' = 2c) (P2/m, 10); [2] P112/m (a' = 2a or b' = 2b or a' = a - b, b' = a + b) (P2/m, 10)

Minimal non-isomorphic supergroups

 I [2] Pmmm (47); [2] Pccm (49); [2] Pmma (51); [2] Pmna (53); [2] Pbam (55); [2] Pnnm (58); [2] Cmmm (65); [2] Cccm (66); [2] P4/m (83); [2] P42/m (84); [3] P6/m (175)
 II [2] A112/m (C2/m, 12); [2] B112/m (C2/m, 12); [2] I112/m (C2/m, 12)