## SgInfo - Space group Info

`sginfo `

```
Extensions
----------
Monoclinic             unique axis b   unique axis c   unique axis a
abc   c-ba      abc   ba-c      abc   -acb
------------    ------------    ------------
cell choice 1   :b1   :-b1      :c1   :-c1      :a1   :-a1
2   :b2   :-b2      :c2   :-c2      :a2   :-a2
3   :b3   :-b3      :c3   :-c3      :a3   :-a3

Orthorhombic   :ba-c    change of basis abc -> ba-c
:1       origin choice 1
:2ba-c   origin choice 2, change of basis abc -> ba-c

Tetragonal     :1       origin choice 1
Cubic   :2       origin choice 2

Trigonal       :H       hexagonal    axes
:R       rhombohedral axes

Number   Schoenflies   Hermann-Mauguin             Hall
------   -----------   ---------------             ----
1        C1^1          P1                           P 1
2        Ci^1          P-1                         -P 1
3:b      C2^1          P2:b = P121                  P 2y
3:c      C2^1          P2:c = P112                  P 2
3:a      C2^1          P2:a = P211                  P 2x
4:b      C2^2          P21:b = P1211                P 2yb
4:c      C2^2          P21:c = P1121                P 2c
4:a      C2^2          P21:a = P2111                P 2xa
5:b1     C2^3          C2:b1 = C121                 C 2y
5:b2     C2^3          C2:b2 = A121                 A 2y
5:b3     C2^3          C2:b3 = I121                 I 2y
5:c1     C2^3          C2:c1 = A112                 A 2
5:c2     C2^3          C2:c2 = B112 = B2            B 2
5:c3     C2^3          C2:c3 = I112                 I 2
5:a1     C2^3          C2:a1 = B211                 B 2x
5:a2     C2^3          C2:a2 = C211                 C 2x
5:a3     C2^3          C2:a3 = I211                 I 2x
6:b      Cs^1          Pm:b = P1m1                  P -2y
6:c      Cs^1          Pm:c = P11m                  P -2
6:a      Cs^1          Pm:a = Pm11                  P -2x
7:b1     Cs^2          Pc:b1 = P1c1                 P -2yc
7:b2     Cs^2          Pc:b2 = P1n1                 P -2yac
7:b3     Cs^2          Pc:b3 = P1a1                 P -2ya
7:c1     Cs^2          Pc:c1 = P11a                 P -2a
7:c2     Cs^2          Pc:c2 = P11n                 P -2ab
7:c3     Cs^2          Pc:c3 = P11b = Pb            P -2b
7:a1     Cs^2          Pc:a1 = Pb11                 P -2xb
7:a2     Cs^2          Pc:a2 = Pn11                 P -2xbc
7:a3     Cs^2          Pc:a3 = Pc11                 P -2xc
8:b1     Cs^3          Cm:b1 = C1m1                 C -2y
8:b2     Cs^3          Cm:b2 = A1m1                 A -2y
8:b3     Cs^3          Cm:b3 = I1m1                 I -2y
8:c1     Cs^3          Cm:c1 = A11m                 A -2
8:c2     Cs^3          Cm:c2 = B11m = Bm            B -2
8:c3     Cs^3          Cm:c3 = I11m                 I -2
8:a1     Cs^3          Cm:a1 = Bm11                 B -2x
8:a2     Cs^3          Cm:a2 = Cm11                 C -2x
8:a3     Cs^3          Cm:a3 = Im11                 I -2x
9:b1     Cs^4          Cc:b1 = C1c1                 C -2yc
9:b2     Cs^4          Cc:b2 = A1n1                 A -2yac
9:b3     Cs^4          Cc:b3 = I1a1                 I -2ya
9:-b1    Cs^4          Cc:-b1 = A1a1                A -2ya
9:-b2    Cs^4          Cc:-b2 = C1n1                C -2ybc
9:-b3    Cs^4          Cc:-b3 = I1c1                I -2yc
9:c1     Cs^4          Cc:c1 = A11a                 A -2a
9:c2     Cs^4          Cc:c2 = B11n                 B -2bc
9:c3     Cs^4          Cc:c3 = I11b                 I -2b
9:-c1    Cs^4          Cc:-c1 = B11b = Bb           B -2b
9:-c2    Cs^4          Cc:-c2 = A11n                A -2ac
9:-c3    Cs^4          Cc:-c3 = I11a                I -2a
9:a1     Cs^4          Cc:a1 = Bb11                 B -2xb
9:a2     Cs^4          Cc:a2 = Cn11                 C -2xbc
9:a3     Cs^4          Cc:a3 = Ic11                 I -2xc
9:-a1    Cs^4          Cc:-a1 = Cc11                C -2xc
9:-a2    Cs^4          Cc:-a2 = Bn11                B -2xbc
9:-a3    Cs^4          Cc:-a3 = Ib11                I -2xb
10:b      C2h^1         P2/m:b = P12/m1             -P 2y
10:c      C2h^1         P2/m:c = P112/m             -P 2
10:a      C2h^1         P2/m:a = P2/m11             -P 2x
11:b      C2h^2         P21/m:b = P121/m1           -P 2yb
11:c      C2h^2         P21/m:c = P1121/m           -P 2c
11:a      C2h^2         P21/m:a = P21/m11           -P 2xa
12:b1     C2h^3         C2/m:b1 = C12/m1            -C 2y
12:b2     C2h^3         C2/m:b2 = A12/m1            -A 2y
12:b3     C2h^3         C2/m:b3 = I12/m1            -I 2y
12:c1     C2h^3         C2/m:c1 = A112/m            -A 2
12:c2     C2h^3         C2/m:c2 = B112/m = B2/m     -B 2
12:c3     C2h^3         C2/m:c3 = I112/m            -I 2
12:a1     C2h^3         C2/m:a1 = B2/m11            -B 2x
12:a2     C2h^3         C2/m:a2 = C2/m11            -C 2x
12:a3     C2h^3         C2/m:a3 = I2/m11            -I 2x
13:b1     C2h^4         P2/c:b1 = P12/c1            -P 2yc
13:b2     C2h^4         P2/c:b2 = P12/n1            -P 2yac
13:b3     C2h^4         P2/c:b3 = P12/a1            -P 2ya
13:c1     C2h^4         P2/c:c1 = P112/a            -P 2a
13:c2     C2h^4         P2/c:c2 = P112/n            -P 2ab
13:c3     C2h^4         P2/c:c3 = P112/b = P2/b     -P 2b
13:a1     C2h^4         P2/c:a1 = P2/b11            -P 2xb
13:a2     C2h^4         P2/c:a2 = P2/n11            -P 2xbc
13:a3     C2h^4         P2/c:a3 = P2/c11            -P 2xc
14:b1     C2h^5         P21/c:b1 = P121/c1          -P 2ybc
14:b2     C2h^5         P21/c:b2 = P121/n1          -P 2yn
14:b3     C2h^5         P21/c:b3 = P121/a1          -P 2yab
14:c1     C2h^5         P21/c:c1 = P1121/a          -P 2ac
14:c2     C2h^5         P21/c:c2 = P1121/n          -P 2n
14:c3     C2h^5         P21/c:c3 = P1121/b = P21/b  -P 2bc
14:a1     C2h^5         P21/c:a1 = P21/b11          -P 2xab
14:a2     C2h^5         P21/c:a2 = P21/n11          -P 2xn
14:a3     C2h^5         P21/c:a3 = P21/c11          -P 2xac
15:b1     C2h^6         C2/c:b1 = C12/c1            -C 2yc
15:b2     C2h^6         C2/c:b2 = A12/n1            -A 2yac
15:b3     C2h^6         C2/c:b3 = I12/a1            -I 2ya
15:-b1    C2h^6         C2/c:-b1 = A12/a1           -A 2ya
15:-b2    C2h^6         C2/c:-b2 = C12/n1           -C 2ybc
15:-b3    C2h^6         C2/c:-b3 = I12/c1           -I 2yc
15:c1     C2h^6         C2/c:c1 = A112/a            -A 2a
15:c2     C2h^6         C2/c:c2 = B112/n            -B 2bc
15:c3     C2h^6         C2/c:c3 = I112/b            -I 2b
15:-c1    C2h^6         C2/c:-c1 = B112/b = B2/b    -B 2b
15:-c2    C2h^6         C2/c:-c2 = A112/n           -A 2ac
15:-c3    C2h^6         C2/c:-c3 = I112/a           -I 2a
15:a1     C2h^6         C2/c:a1 = B2/b11            -B 2xb
15:a2     C2h^6         C2/c:a2 = C2/n11            -C 2xbc
15:a3     C2h^6         C2/c:a3 = I2/c11            -I 2xc
15:-a1    C2h^6         C2/c:-a1 = C2/c11           -C 2xc
15:-a2    C2h^6         C2/c:-a2 = B2/n11           -B 2xbc
15:-a3    C2h^6         C2/c:-a3 = I2/b11           -I 2xb
16        D2^1          P222                         P 2 2
17        D2^2          P2221                        P 2c 2
17:cab    D2^2          P2122                        P 2a 2a
17:bca    D2^2          P2212                        P 2 2b
18        D2^3          P21212                       P 2 2ab
18:cab    D2^3          P22121                       P 2bc 2
18:bca    D2^3          P21221                       P 2ac 2ac
19        D2^4          P212121                      P 2ac 2ab
20        D2^5          C2221                        C 2c 2
20:cab    D2^5          A2122                        A 2a 2a
20:bca    D2^5          B2212                        B 2 2b
21        D2^6          C222                         C 2 2
21:cab    D2^6          A222                         A 2 2
21:bca    D2^6          B222                         B 2 2
22        D2^7          F222                         F 2 2
23        D2^8          I222                         I 2 2
24        D2^9          I212121                      I 2b 2c
25        C2v^1         Pmm2                         P 2 -2
25:cab    C2v^1         P2mm                         P -2 2
25:bca    C2v^1         Pm2m                         P -2 -2
26        C2v^2         Pmc21                        P 2c -2
26:ba-c   C2v^2         Pcm21                        P 2c -2c
26:cab    C2v^2         P21ma                        P -2a 2a
26:-cba   C2v^2         P21am                        P -2 2a
26:bca    C2v^2         Pb21m                        P -2 -2b
26:a-cb   C2v^2         Pm21b                        P -2b -2
27        C2v^3         Pcc2                         P 2 -2c
27:cab    C2v^3         P2aa                         P -2a 2
27:bca    C2v^3         Pb2b                         P -2b -2b
28        C2v^4         Pma2                         P 2 -2a
28:ba-c   C2v^4         Pbm2                         P 2 -2b
28:cab    C2v^4         P2mb                         P -2b 2
28:-cba   C2v^4         P2cm                         P -2c 2
28:bca    C2v^4         Pc2m                         P -2c -2c
28:a-cb   C2v^4         Pm2a                         P -2a -2a
29        C2v^5         Pca21                        P 2c -2ac
29:ba-c   C2v^5         Pbc21                        P 2c -2b
29:cab    C2v^5         P21ab                        P -2b 2a
29:-cba   C2v^5         P21ca                        P -2ac 2a
29:bca    C2v^5         Pc21b                        P -2bc -2c
29:a-cb   C2v^5         Pb21a                        P -2a -2ab
30        C2v^6         Pnc2                         P 2 -2bc
30:ba-c   C2v^6         Pcn2                         P 2 -2ac
30:cab    C2v^6         P2na                         P -2ac 2
30:-cba   C2v^6         P2an                         P -2ab 2
30:bca    C2v^6         Pb2n                         P -2ab -2ab
30:a-cb   C2v^6         Pn2b                         P -2bc -2bc
31        C2v^7         Pmn21                        P 2ac -2
31:ba-c   C2v^7         Pnm21                        P 2bc -2bc
31:cab    C2v^7         P21mn                        P -2ab 2ab
31:-cba   C2v^7         P21nm                        P -2 2ac
31:bca    C2v^7         Pn21m                        P -2 -2bc
31:a-cb   C2v^7         Pm21n                        P -2ab -2
32        C2v^8         Pba2                         P 2 -2ab
32:cab    C2v^8         P2cb                         P -2bc 2
32:bca    C2v^8         Pc2a                         P -2ac -2ac
33        C2v^9         Pna21                        P 2c -2n
33:ba-c   C2v^9         Pbn21                        P 2c -2ab
33:cab    C2v^9         P21nb                        P -2bc 2a
33:-cba   C2v^9         P21cn                        P -2n 2a
33:bca    C2v^9         Pc21n                        P -2n -2ac
33:a-cb   C2v^9         Pn21a                        P -2ac -2n
34        C2v^10        Pnn2                         P 2 -2n
34:cab    C2v^10        P2nn                         P -2n 2
34:bca    C2v^10        Pn2n                         P -2n -2n
35        C2v^11        Cmm2                         C 2 -2
35:cab    C2v^11        A2mm                         A -2 2
35:bca    C2v^11        Bm2m                         B -2 -2
36        C2v^12        Cmc21                        C 2c -2
36:ba-c   C2v^12        Ccm21                        C 2c -2c
36:cab    C2v^12        A21ma                        A -2a 2a
36:-cba   C2v^12        A21am                        A -2 2a
36:bca    C2v^12        Bb21m                        B -2 -2b
36:a-cb   C2v^12        Bm21b                        B -2b -2
37        C2v^13        Ccc2                         C 2 -2c
37:cab    C2v^13        A2aa                         A -2a 2
37:bca    C2v^13        Bb2b                         B -2b -2b
38        C2v^14        Amm2                         A 2 -2
38:ba-c   C2v^14        Bmm2                         B 2 -2
38:cab    C2v^14        B2mm                         B -2 2
38:-cba   C2v^14        C2mm                         C -2 2
38:bca    C2v^14        Cm2m                         C -2 -2
38:a-cb   C2v^14        Am2m                         A -2 -2
39        C2v^15        Abm2                         A 2 -2c
39:ba-c   C2v^15        Bma2                         B 2 -2c
39:cab    C2v^15        B2cm                         B -2c 2
39:-cba   C2v^15        C2mb                         C -2b 2
39:bca    C2v^15        Cm2a                         C -2b -2b
39:a-cb   C2v^15        Ac2m                         A -2c -2c
40        C2v^16        Ama2                         A 2 -2a
40:ba-c   C2v^16        Bbm2                         B 2 -2b
40:cab    C2v^16        B2mb                         B -2b 2
40:-cba   C2v^16        C2cm                         C -2c 2
40:bca    C2v^16        Cc2m                         C -2c -2c
40:a-cb   C2v^16        Am2a                         A -2a -2a
41        C2v^17        Aba2                         A 2 -2ac
41:ba-c   C2v^17        Bba2                         B 2 -2bc
41:cab    C2v^17        B2cb                         B -2bc 2
41:-cba   C2v^17        C2cb                         C -2bc 2
41:bca    C2v^17        Cc2a                         C -2bc -2bc
41:a-cb   C2v^17        Ac2a                         A -2ac -2ac
42        C2v^18        Fmm2                         F 2 -2
42:cab    C2v^18        F2mm                         F -2 2
42:bca    C2v^18        Fm2m                         F -2 -2
43        C2v^19        Fdd2                         F 2 -2d
43:cab    C2v^19        F2dd                         F -2d 2
43:bca    C2v^19        Fd2d                         F -2d -2d
44        C2v^20        Imm2                         I 2 -2
44:cab    C2v^20        I2mm                         I -2 2
44:bca    C2v^20        Im2m                         I -2 -2
45        C2v^21        Iba2                         I 2 -2c
45:cab    C2v^21        I2cb                         I -2a 2
45:bca    C2v^21        Ic2a                         I -2b -2b
46        C2v^22        Ima2                         I 2 -2a
46:ba-c   C2v^22        Ibm2                         I 2 -2b
46:cab    C2v^22        I2mb                         I -2b 2
46:-cba   C2v^22        I2cm                         I -2c 2
46:bca    C2v^22        Ic2m                         I -2c -2c
46:a-cb   C2v^22        Im2a                         I -2a -2a
47        D2h^1         Pmmm                        -P 2 2
48:1      D2h^2         Pnnn:1                       P 2 2 -1n
48:2      D2h^2         Pnnn:2                      -P 2ab 2bc
49        D2h^3         Pccm                        -P 2 2c
49:cab    D2h^3         Pmaa                        -P 2a 2
49:bca    D2h^3         Pbmb                        -P 2b 2b
50:1      D2h^4         Pban:1                       P 2 2 -1ab
50:2      D2h^4         Pban:2                      -P 2ab 2b
50:1cab   D2h^4         Pncb:1                       P 2 2 -1bc
50:2cab   D2h^4         Pncb:2                      -P 2b 2bc
50:1bca   D2h^4         Pcna:1                       P 2 2 -1ac
50:2bca   D2h^4         Pcna:2                      -P 2a 2c
51        D2h^5         Pmma                        -P 2a 2a
51:ba-c   D2h^5         Pmmb                        -P 2b 2
51:cab    D2h^5         Pbmm                        -P 2 2b
51:-cba   D2h^5         Pcmm                        -P 2c 2c
51:bca    D2h^5         Pmcm                        -P 2c 2
51:a-cb   D2h^5         Pmam                        -P 2 2a
52        D2h^6         Pnna                        -P 2a 2bc
52:ba-c   D2h^6         Pnnb                        -P 2b 2n
52:cab    D2h^6         Pbnn                        -P 2n 2b
52:-cba   D2h^6         Pcnn                        -P 2ab 2c
52:bca    D2h^6         Pncn                        -P 2ab 2n
52:a-cb   D2h^6         Pnan                        -P 2n 2bc
53        D2h^7         Pmna                        -P 2ac 2
53:ba-c   D2h^7         Pnmb                        -P 2bc 2bc
53:cab    D2h^7         Pbmn                        -P 2ab 2ab
53:-cba   D2h^7         Pcnm                        -P 2 2ac
53:bca    D2h^7         Pncm                        -P 2 2bc
53:a-cb   D2h^7         Pman                        -P 2ab 2
54        D2h^8         Pcca                        -P 2a 2ac
54:ba-c   D2h^8         Pccb                        -P 2b 2c
54:cab    D2h^8         Pbaa                        -P 2a 2b
54:-cba   D2h^8         Pcaa                        -P 2ac 2c
54:bca    D2h^8         Pbcb                        -P 2bc 2b
54:a-cb   D2h^8         Pbab                        -P 2b 2ab
55        D2h^9         Pbam                        -P 2 2ab
55:cab    D2h^9         Pmcb                        -P 2bc 2
55:bca    D2h^9         Pcma                        -P 2ac 2ac
56        D2h^10        Pccn                        -P 2ab 2ac
56:cab    D2h^10        Pnaa                        -P 2ac 2bc
56:bca    D2h^10        Pbnb                        -P 2bc 2ab
57        D2h^11        Pbcm                        -P 2c 2b
57:ba-c   D2h^11        Pcam                        -P 2c 2ac
57:cab    D2h^11        Pmca                        -P 2ac 2a
57:-cba   D2h^11        Pmab                        -P 2b 2a
57:bca    D2h^11        Pbma                        -P 2a 2ab
57:a-cb   D2h^11        Pcmb                        -P 2bc 2c
58        D2h^12        Pnnm                        -P 2 2n
58:cab    D2h^12        Pmnn                        -P 2n 2
58:bca    D2h^12        Pnmn                        -P 2n 2n
59:1      D2h^13        Pmmn:1                       P 2 2ab -1ab
59:2      D2h^13        Pmmn:2                      -P 2ab 2a
59:1cab   D2h^13        Pnmm:1                       P 2bc 2 -1bc
59:2cab   D2h^13        Pnmm:2                      -P 2c 2bc
59:1bca   D2h^13        Pmnm:1                       P 2ac 2ac -1ac
59:2bca   D2h^13        Pmnm:2                      -P 2c 2a
60        D2h^14        Pbcn                        -P 2n 2ab
60:ba-c   D2h^14        Pcan                        -P 2n 2c
60:cab    D2h^14        Pnca                        -P 2a 2n
60:-cba   D2h^14        Pnab                        -P 2bc 2n
60:bca    D2h^14        Pbna                        -P 2ac 2b
60:a-cb   D2h^14        Pcnb                        -P 2b 2ac
61        D2h^15        Pbca                        -P 2ac 2ab
61:ba-c   D2h^15        Pcab                        -P 2bc 2ac
62        D2h^16        Pnma                        -P 2ac 2n
62:ba-c   D2h^16        Pmnb                        -P 2bc 2a
62:cab    D2h^16        Pbnm                        -P 2c 2ab
62:-cba   D2h^16        Pcmn                        -P 2n 2ac
62:bca    D2h^16        Pmcn                        -P 2n 2a
62:a-cb   D2h^16        Pnam                        -P 2c 2n
63        D2h^17        Cmcm                        -C 2c 2
63:ba-c   D2h^17        Ccmm                        -C 2c 2c
63:cab    D2h^17        Amma                        -A 2a 2a
63:-cba   D2h^17        Amam                        -A 2 2a
63:bca    D2h^17        Bbmm                        -B 2 2b
63:a-cb   D2h^17        Bmmb                        -B 2b 2
64        D2h^18        Cmca                        -C 2bc 2
64:ba-c   D2h^18        Ccmb                        -C 2bc 2bc
64:cab    D2h^18        Abma                        -A 2ac 2ac
64:-cba   D2h^18        Acam                        -A 2 2ac
64:bca    D2h^18        Bbcm                        -B 2 2bc
64:a-cb   D2h^18        Bmab                        -B 2bc 2
65        D2h^19        Cmmm                        -C 2 2
65:cab    D2h^19        Ammm                        -A 2 2
65:bca    D2h^19        Bmmm                        -B 2 2
66        D2h^20        Cccm                        -C 2 2c
66:cab    D2h^20        Amaa                        -A 2a 2
66:bca    D2h^20        Bbmb                        -B 2b 2b
67        D2h^21        Cmma                        -C 2b 2
67:ba-c   D2h^21        Cmmb                        -C 2b 2b
67:cab    D2h^21        Abmm                        -A 2c 2c
67:-cba   D2h^21        Acmm                        -A 2 2c
67:bca    D2h^21        Bmcm                        -B 2 2c
67:a-cb   D2h^21        Bmam                        -B 2c 2
68:1      D2h^22        Ccca:1                       C 2 2 -1bc
68:2      D2h^22        Ccca:2                      -C 2b 2bc
68:1ba-c  D2h^22        Cccb:1                       C 2 2 -1bc
68:2ba-c  D2h^22        Cccb:2                      -C 2b 2c
68:1cab   D2h^22        Abaa:1                       A 2 2 -1ac
68:2cab   D2h^22        Abaa:2                      -A 2a 2c
68:1-cba  D2h^22        Acaa:1                       A 2 2 -1ac
68:2-cba  D2h^22        Acaa:2                      -A 2ac 2c
68:1bca   D2h^22        Bbcb:1                       B 2 2 -1bc
68:2bca   D2h^22        Bbcb:2                      -B 2bc 2b
68:1a-cb  D2h^22        Bbab:1                       B 2 2 -1bc
68:2a-cb  D2h^22        Bbab:2                      -B 2b 2bc
69        D2h^23        Fmmm                        -F 2 2
70:1      D2h^24        Fddd:1                       F 2 2 -1d
70:2      D2h^24        Fddd:2                      -F 2uv 2vw
71        D2h^25        Immm                        -I 2 2
72        D2h^26        Ibam                        -I 2 2c
72:cab    D2h^26        Imcb                        -I 2a 2
72:bca    D2h^26        Icma                        -I 2b 2b
73        D2h^27        Ibca                        -I 2b 2c
73:ba-c   D2h^27        Icab                        -I 2a 2b
74        D2h^28        Imma                        -I 2b 2
74:ba-c   D2h^28        Immb                        -I 2a 2a
74:cab    D2h^28        Ibmm                        -I 2c 2c
74:-cba   D2h^28        Icmm                        -I 2 2b
74:bca    D2h^28        Imcm                        -I 2 2a
74:a-cb   D2h^28        Imam                        -I 2c 2
75        C4^1          P4                           P 4
76        C4^2          P41                          P 4w
77        C4^3          P42                          P 4c
78        C4^4          P43                          P 4cw
79        C4^5          I4                           I 4
80        C4^6          I41                          I 4bw
81        S4^1          P-4                          P -4
82        S4^2          I-4                          I -4
83        C4h^1         P4/m                        -P 4
84        C4h^2         P42/m                       -P 4c
85:1      C4h^3         P4/n:1                       P 4ab -1ab
85:2      C4h^3         P4/n:2                      -P 4a
86:1      C4h^4         P42/n:1                      P 4n -1n
86:2      C4h^4         P42/n:2                     -P 4bc
87        C4h^5         I4/m                        -I 4
88:1      C4h^6         I41/a:1                      I 4bw -1bw
89        D4^1          P422                         P 4 2
90        D4^2          P4212                        P 4ab 2ab
91        D4^3          P4122                        P 4w 2c
92        D4^4          P41212                       P 4abw 2nw
93        D4^5          P4222                        P 4c 2
94        D4^6          P42212                       P 4n 2n
95        D4^7          P4322                        P 4cw 2c
96        D4^8          P43212                       P 4nw 2abw
97        D4^9          I422                         I 4 2
98        D4^10         I4122                        I 4bw 2bw
99        C4v^1         P4mm                         P 4 -2
100        C4v^2         P4bm                         P 4 -2ab
101        C4v^3         P42cm                        P 4c -2c
102        C4v^4         P42nm                        P 4n -2n
103        C4v^5         P4cc                         P 4 -2c
104        C4v^6         P4nc                         P 4 -2n
105        C4v^7         P42mc                        P 4c -2
106        C4v^8         P42bc                        P 4c -2ab
107        C4v^9         I4mm                         I 4 -2
108        C4v^10        I4cm                         I 4 -2c
109        C4v^11        I41md                        I 4bw -2
110        C4v^12        I41cd                        I 4bw -2c
111        D2d^1         P-42m                        P -4 2
112        D2d^2         P-42c                        P -4 2c
113        D2d^3         P-421m                       P -4 2ab
114        D2d^4         P-421c                       P -4 2n
115        D2d^5         P-4m2                        P -4 -2
116        D2d^6         P-4c2                        P -4 -2c
117        D2d^7         P-4b2                        P -4 -2ab
118        D2d^8         P-4n2                        P -4 -2n
119        D2d^9         I-4m2                        I -4 -2
120        D2d^10        I-4c2                        I -4 -2c
121        D2d^11        I-42m                        I -4 2
122        D2d^12        I-42d                        I -4 2bw
123        D4h^1         P4/mmm                      -P 4 2
124        D4h^2         P4/mcc                      -P 4 2c
125:1      D4h^3         P4/nbm:1                     P 4 2 -1ab
125:2      D4h^3         P4/nbm:2                    -P 4a 2b
126:1      D4h^4         P4/nnc:1                     P 4 2 -1n
126:2      D4h^4         P4/nnc:2                    -P 4a 2bc
127        D4h^5         P4/mbm                      -P 4 2ab
128        D4h^6         P4/mnc                      -P 4 2n
129:1      D4h^7         P4/nmm:1                     P 4ab 2ab -1ab
129:2      D4h^7         P4/nmm:2                    -P 4a 2a
130:1      D4h^8         P4/ncc:1                     P 4ab 2n -1ab
130:2      D4h^8         P4/ncc:2                    -P 4a 2ac
131        D4h^9         P42/mmc                     -P 4c 2
132        D4h^10        P42/mcm                     -P 4c 2c
133:1      D4h^11        P42/nbc:1                    P 4n 2c -1n
133:2      D4h^11        P42/nbc:2                   -P 4ac 2b
134:1      D4h^12        P42/nnm:1                    P 4n 2 -1n
134:2      D4h^12        P42/nnm:2                   -P 4ac 2bc
135        D4h^13        P42/mbc                     -P 4c 2ab
136        D4h^14        P42/mnm                     -P 4n 2n
137:1      D4h^15        P42/nmc:1                    P 4n 2n -1n
137:2      D4h^15        P42/nmc:2                   -P 4ac 2a
138:1      D4h^16        P42/ncm:1                    P 4n 2ab -1n
138:2      D4h^16        P42/ncm:2                   -P 4ac 2ac
139        D4h^17        I4/mmm                      -I 4 2
140        D4h^18        I4/mcm                      -I 4 2c
141:1      D4h^19        I41/amd:1                    I 4bw 2bw -1bw
141:2      D4h^19        I41/amd:2                   -I 4bd 2
142:1      D4h^20        I41/acd:1                    I 4bw 2aw -1bw
142:2      D4h^20        I41/acd:2                   -I 4bd 2c
143        C3^1          P3                           P 3
144        C3^2          P31                          P 31
145        C3^3          P32                          P 32
146:H      C3^4          R3:H                         R 3
146:R      C3^4          R3:R                         P 3*
147        C3i^1         P-3                         -P 3
148:H      C3i^2         R-3:H                       -R 3
148:R      C3i^2         R-3:R                       -P 3*
149        D3^1          P312                         P 3 2
150        D3^2          P321                         P 3 2"
151        D3^3          P3112                        P 31 2c (0 0 1)
152        D3^4          P3121                        P 31 2"
153        D3^5          P3212                        P 32 2c (0 0 -1)
154        D3^6          P3221                        P 32 2"
155:H      D3^7          R32:H                        R 3 2"
155:R      D3^7          R32:R                        P 3* 2
156        C3v^1         P3m1                         P 3 -2"
157        C3v^2         P31m                         P 3 -2
158        C3v^3         P3c1                         P 3 -2"c
159        C3v^4         P31c                         P 3 -2c
160:H      C3v^5         R3m:H                        R 3 -2"
160:R      C3v^5         R3m:R                        P 3* -2
161:H      C3v^6         R3c:H                        R 3 -2"c
161:R      C3v^6         R3c:R                        P 3* -2n
162        D3d^1         P-31m                       -P 3 2
163        D3d^2         P-31c                       -P 3 2c
164        D3d^3         P-3m1                       -P 3 2"
165        D3d^4         P-3c1                       -P 3 2"c
166:H      D3d^5         R-3m:H                      -R 3 2"
166:R      D3d^5         R-3m:R                      -P 3* 2
167:H      D3d^6         R-3c:H                      -R 3 2"c
167:R      D3d^6         R-3c:R                      -P 3* 2n
168        C6^1          P6                           P 6
169        C6^2          P61                          P 61
170        C6^3          P65                          P 65
171        C6^4          P62                          P 62
172        C6^5          P64                          P 64
173        C6^6          P63                          P 6c
174        C3h^1         P-6                          P -6
175        C6h^1         P6/m                        -P 6
176        C6h^2         P63/m                       -P 6c
177        D6^1          P622                         P 6 2
178        D6^2          P6122                        P 61 2 (0 0 -1)
179        D6^3          P6522                        P 65 2 (0 0 1)
180        D6^4          P6222                        P 62 2c (0 0 1)
181        D6^5          P6422                        P 64 2c (0 0 -1)
182        D6^6          P6322                        P 6c 2c
183        C6v^1         P6mm                         P 6 -2
184        C6v^2         P6cc                         P 6 -2c
185        C6v^3         P63cm                        P 6c -2
186        C6v^4         P63mc                        P 6c -2c
187        D3h^1         P-6m2                        P -6 2
188        D3h^2         P-6c2                        P -6c 2
189        D3h^3         P-62m                        P -6 -2
190        D3h^4         P-62c                        P -6c -2c
191        D6h^1         P6/mmm                      -P 6 2
192        D6h^2         P6/mcc                      -P 6 2c
193        D6h^3         P63/mcm                     -P 6c 2
194        D6h^4         P63/mmc                     -P 6c 2c
195        T^1           P23                          P 2 2 3
196        T^2           F23                          F 2 2 3
197        T^3           I23                          I 2 2 3
198        T^4           P213                         P 2ac 2ab 3
199        T^5           I213                         I 2b 2c 3
200        Th^1          Pm-3                        -P 2 2 3
201:1      Th^2          Pn-3:1                       P 2 2 3 -1n
201:2      Th^2          Pn-3:2                      -P 2ab 2bc 3
202        Th^3          Fm-3                        -F 2 2 3
203:1      Th^4          Fd-3:1                       F 2 2 3 -1d
203:2      Th^4          Fd-3:2                      -F 2uv 2vw 3
204        Th^5          Im-3                        -I 2 2 3
205        Th^6          Pa-3                        -P 2ac 2ab 3
206        Th^7          Ia-3                        -I 2b 2c 3
207        O^1           P432                         P 4 2 3
208        O^2           P4232                        P 4n 2 3
209        O^3           F432                         F 4 2 3
210        O^4           F4132                        F 4d 2 3
211        O^5           I432                         I 4 2 3
212        O^6           P4332                        P 4acd 2ab 3
213        O^7           P4132                        P 4bd 2ab 3
214        O^8           I4132                        I 4bd 2c 3
215        Td^1          P-43m                        P -4 2 3
216        Td^2          F-43m                        F -4 2 3
217        Td^3          I-43m                        I -4 2 3
218        Td^4          P-43n                        P -4n 2 3
219        Td^5          F-43c                        F -4c 2 3
220        Td^6          I-43d                        I -4bd 2c 3
221        Oh^1          Pm-3m                       -P 4 2 3
222:1      Oh^2          Pn-3n:1                      P 4 2 3 -1n
222:2      Oh^2          Pn-3n:2                     -P 4a 2bc 3
223        Oh^3          Pm-3n                       -P 4n 2 3
224:1      Oh^4          Pn-3m:1                      P 4n 2 3 -1n
224:2      Oh^4          Pn-3m:2                     -P 4bc 2bc 3
225        Oh^5          Fm-3m                       -F 4 2 3
226        Oh^6          Fm-3c                       -F 4c 2 3
227:1      Oh^7          Fd-3m:1                      F 4d 2 3 -1d
227:2      Oh^7          Fd-3m:2                     -F 4vw 2vw 3
228:1      Oh^8          Fd-3c:1                      F 4d 2 3 -1cd
228:2      Oh^8          Fd-3c:2                     -F 4cvw 2vw 3
229        Oh^9          Im-3m                       -I 4 2 3
230        Oh^10         Ia-3d                       -I 4bd 2c 3

```