P21 C22 2 Monoclinic No. 4 P1211 Patterson symmetry P12/m1 UNIQUE AXIS b

Origin on 21

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

Symmetry operations

 (1)  1 (2)  2(0, 1/2, 0)   0, y, 0

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) -x, y + 1/2, -z
0k0 : k = 2n

Symmetry of special projections

 Along [001]   p1g1a' = ap   b' = b   Origin at 0, 0, z Along [100]   p11ga' = 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] P1 (1) 1
 IIa none
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [2] P1211 (c' = 2c or a' = 2a or a' = a + c, c' = -a + c) (P21, 4); [3] P1211 (b' = 3b) (P21, 4)

Minimal non-isomorphic supergroups

 I [2] P21/m (11); [2] P21/c (14); [2] P2221 (17); [2] P21212 (18); [2] P212121 (19); [2] C2221 (20); [2] Pmc21 (26); [2] Pca21 (29); [2] Pmn21 (31); [2] Pna21 (33); [2] Cmc21 (36); [2] P41 (76); [2] P43 (78); [3] P61 (169); [3] P65 (170); [3] P63 (173)
 II [2] C121 (C2, 5); [2] A121 (C2, 5); [2] I121 (C2, 5); [2] P121 (b' = 1/2b) (P2, 3)

 P21 C22 2 Monoclinic No. 4 P1121 Patterson symmetry P112/m UNIQUE AXIS c

Origin on 21

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

Symmetry operations

 (1)  1 (2)  2(0, 0, 1/2)   0, 0, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) -x, -y, z + 1/2
00l : l = 2n

Symmetry of special projections

 Along [001]   p2a' = a   b' = b   Origin at 0, 0, z Along [100]   p1g1a' = bp   b' = c   Origin at x, 0, 0 Along [010]   p11ga' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [2] P1121 (a' = 2a or b' = 2b or a' = a - b, b' = a + b) (P21, 4); [3] P1121 (c' = 3c) (P21, 4)

Minimal non-isomorphic supergroups

 I [2] P21/m (11); [2] P21/c (14); [2] P2221 (17); [2] P21212 (18); [2] P212121 (19); [2] C2221 (20); [2] Pmc21 (26); [2] Pca21 (29); [2] Pmn21 (31); [2] Pna21 (33); [2] Cmc21 (36); [2] P41 (76); [2] P43 (78); [3] P61 (169); [3] P65 (170); [3] P63 (173)
 II [2] A112 (C2, 5); [2] B112 (C2, 5); [2] I112 (C2, 5); [2] P112 (c' = 1/2c) (P2, 3)