P21/m C2h2 2/m Monoclinic No. 11 P121/m1 Patterson symmetry P12/m1 UNIQUE AXIS b

Origin at -1 on 21

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Symmetry operations

 (1)  1 (2)  2(0, 1/2, 0)   0, y, 0 (3)  -1   0, 0, 0 (4)  m   x, 1/4, 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 f 1
 (1) x, y, z (2) -x, y + 1/2, -z (3) -x, -y, -z (4) x, -y + 1/2, z
0k0 : k = 2n
Special: as above, plus
 2 e m
 x, 1/4, z -x, 3/4, -z
no extra conditions
 2 d -1
 1/2, 0, 1/2 1/2, 1/2, 1/2
hkl : k = 2n
 2 c -1
 0, 0, 1/2 0, 1/2, 1/2
hkl : k = 2n
 2 b -1
 1/2, 0, 0 1/2, 1/2, 0
hkl : k = 2n
 2 a -1
 0, 0, 0 0, 1/2, 0
hkl : k = 2n

Symmetry of special projections

 Along [001]   p2gma' = ap   b' = b   Origin at 0, 0, z Along [100]   p2mga' = 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] P1211 (P21, 4) 1; 2 [2] P-1 (2) 1; 3
 IIa none
 IIb [2] P121/c1 (c' = 2c) (P21/c, 14); [2] P121/a1 (a' = 2a) (P21/c, 14); [2] B121/e1 (a' = 2a, c' = 2c) (P21/c, 14)

Maximal isomorphic subgroups of lowest index

 IIc [2] P121/m1 (c' = 2c or a' = 2a or a' = a + c, c' = -a + c) (P21/m, 11); [3] P121/m1 (b' = 3b) (P21/m, 11)

Minimal non-isomorphic supergroups

 I [2] Pmma (51); [2] Pbcm (57); [2] Pmmn (59); [2] Pnma (62); [2] Cmcm (63); [3] P63/m (176)
 II [2] C12/m1 (C2/m, 12); [2] A12/m1 (C2/m, 12); [2] I12/m1 (C2/m, 12); [2] P12/m1 (b' = 1/2b) (P2/m, 10)

 P21/m C2h2 2/m Monoclinic No. 11 P1121/m Patterson symmetry P112/m UNIQUE AXIS c

Origin at -1 on 21

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Symmetry operations

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

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 f 1
 (1) x, y, z (2) -x, -y, z + 1/2 (3) -x, -y, -z (4) x, y, -z + 1/2
00l : l = 2n
Special: as above, plus
 2 e m
 x, y, 1/4 -x, -y, 3/4
no extra conditions
 2 d -1
 1/2, 1/2, 0 1/2, 1/2, 1/2
hkl : l = 2n
 2 c -1
 1/2, 0, 0 1/2, 0, 1/2
hkl : l = 2n
 2 b -1
 0, 1/2, 0 0, 1/2, 1/2
hkl : l = 2n
 2 a -1
 0, 0, 0 0, 0, 1/2
hkl : l = 2n

Symmetry of special projections

 Along [001]   p2a' = a   b' = b   Origin at 0, 0, z Along [100]   p2gma' = bp   b' = c   Origin at x, 0, 0 Along [010]   p2mga' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P11m (Pm, 6) 1; 4 [2] P1121 (P21, 4) 1; 2 [2] P-1 (2) 1; 3
 IIa none
 IIb [2] P1121/a (a' = 2a) (P21/c, 14); [2] P1121/b (b' = 2b) (P21/c, 14); [2] C1121/e (a' = 2a, b' = 2b) (P21/c, 14)

Maximal isomorphic subgroups of lowest index

 IIc [2] P1121/m (a' = 2a or b' = 2b or a' = a - b, b' = a + b) (P21/m, 11); [3] P1121/m (c' = 3c) (P21/m, 11)

Minimal non-isomorphic supergroups

 I [2] Pmma (51); [2] Pbcm (57); [2] Pmmn (59); [2] Pnma (62); [2] Cmcm (63); [3] P63/m (176)
 II [2] A112/m (C2/m, 12); [2] B112/m (C2/m, 12); [2] I112/m (C2/m, 12); [2] P112/m (c' = 1/2c) (P2/m, 10)