P2 C21 2 Monoclinic No. 3 P121 Patterson symmetry P12/m1 UNIQUE AXIS b

Origin on 2

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

Symmetry operations

 (1)  1 (2)  2   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 e 1
 (1) x, y, z (2) -x, y, -z
no conditions
Special: as above, plus
 1 d 2
 1/2, y, 1/2
no extra conditions
 1 c 2
 1/2, y, 0
no extra conditions
 1 b 2
 0, y, 1/2
no extra conditions
 1 a 2
 0, y, 0
no extra conditions

Symmetry of special projections

 Along [001]   p1m1a' = ap   b' = b   Origin at 0, 0, z Along [100]   p11ma' = 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 [2] P1211 (b' = 2b) (P21, 4); [2] C121 (a' = 2a, b' = 2b) (C2, 5); [2] A121 (b' = 2b, c' = 2c) (C2, 5); [2] F121 (a' = 2a, b' = 2b, c' = 2c) (C2, 5)

Maximal isomorphic subgroups of lowest index

 IIc [2] P121 (b' = 2b) (P2, 3); [2] P121 (c' = 2c or a' = 2a or a' = a + c, c' = -a + c) (P2, 3)

Minimal non-isomorphic supergroups

 I [2] P2/m (10); [2] P2/c (13); [2] P222 (16); [2] P2221 (17); [2] P21212 (18); [2] C222 (21); [2] Pmm2 (25); [2] Pcc2 (27); [2] Pma2 (28); [2] Pnc2 (30); [2] Pba2 (32); [2] Pnn2 (34); [2] Cmm2 (35); [2] Ccc2 (37); [2] P4 (75); [2] P42 (77); [2] P-4 (81); [3] P6 (168); [3] P62 (171); [3] P64 (172)
 II [2] C121 (C2, 5); [2] A121 (C2, 5); [2] I121 (C2, 5)

 P2 C21 2 Monoclinic No. 3 P112 Patterson symmetry P112/m UNIQUE AXIS c

Origin on 2

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

Symmetry operations

 (1)  1 (2)  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 e 1
 (1) x, y, z (2) -x, -y, z
no conditions
Special: as above, plus
 1 d 2
 1/2, 1/2, z
no extra conditions
 1 c 2
 0, 1/2, z
no extra conditions
 1 b 2
 1/2, 0, z
no extra conditions
 1 a 2
 0, 0, z
no extra conditions

Symmetry of special projections

 Along [001]   p2a' = a   b' = b   Origin at 0, 0, z Along [100]   p1m1a' = bp   b' = c   Origin at x, 0, 0 Along [010]   p11ma' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb [2] P1121 (c' = 2c) (P21, 4); [2] A112 (b' = 2b, c' = 2c) (C2, 5); [2] B112 (a' = 2a, c' = 2c) (C2, 5); [2] F112 (a' = 2a, b' = 2b, c' = 2c) (C2, 5)

Maximal isomorphic subgroups of lowest index

 IIc [2] P112 (c' = 2c) (P2, 3); [2] P112 (a' = 2a or b' = 2b or a' = a - b, b' = a + b) (P2, 3)

Minimal non-isomorphic supergroups

 I [2] P2/m (10); [2] P2/c (13); [2] P222 (16); [2] P2221 (17); [2] P21212 (18); [2] C222 (21); [2] Pmm2 (25); [2] Pcc2 (27); [2] Pma2 (28); [2] Pnc2 (30); [2] Pba2 (32); [2] Pnn2 (34); [2] Cmm2 (35); [2] Ccc2 (37); [2] P4 (75); [2] P42 (77); [2] P-4 (81); [3] P6 (168); [3] P62 (171); [3] P64 (172)
 II [2] A112 (C2, 5); [2] B112 (C2, 5); [2] I112 (C2, 5)