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