International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 9.7, pp. 899-901

Table 9.7.1.2 

A. J. C. Wilson,a V. L. Karenb and A. Mighellb

aSt John's College, Cambridge CB2 1TP, England, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

Table 9.7.1.2| top | pdf |
Space groups arranged by arithmetic crystal class and degree of symmorphism (Wilson, 1993d[link]), as frequented by homomolecular structures with one molecule in the general position (in superscript numerals; according to Belsky, Zorkaya & Zorky, 1995[link])

(a) Triclinic, monoclinic and orthorhombic systems. The triclinic space groups are a special case, with `degree of symmorphism' undefined, and they are not assigned to any particular column. For *, † see Subsection 9.7.4.1[link].

Arithmetic crystal classFully symmorphicTending to symmorphismEqually balancedTending to antimorphismFully antimorphic
1P *P1†(90)
[\overline {1}P] *P[{\overline 1}](1796)
2P *P2(0) [\cdots] [\cdots] [\cdots] P21(1327)
2C [\cdots] [\cdots] *C2 †(109) [\cdots] [\cdots]
mP *Pm(0) [\cdots] [\cdots] [\cdots] Pc(58)
mC [\cdots] [\cdots] *Cm(0) [\cdots] Cc(144)
2/mP *P2/m(0) [\cdots] P21/m(0) [\cdots] P21/c(5951)
    P2/c(11)    
2/mC [\cdots] [\cdots] *C2/m(0) C2/c(587) [\cdots]
222P *P222(0) P2221(0) [\cdots] P21212(30) P212121(2795)
222C [\cdots] *C222(0) [\cdots] C2221(11) [\cdots]
222F [\cdots] [\cdots] *F222(0) [\cdots] [\cdots]
222I [\cdots] [\cdots] *I222(0) [\cdots] [\cdots]
    I212121(0)    
mm2P *Pmm2(0) Pma2(0) [\cdots] Pmc21(0) Pca21(153)
      Pcc2(1) Pna21(367)
      Pnc2(1)  
      Pmn21(0)  
      Pba2(1)  
      Pnn2(1)  
mm2C [\cdots] *Cmm2(0) [\cdots] Cmc21(0) [\cdots]
      Ccc2(0)  
2mmC [\cdots] *Amm2(0) [\cdots] Abm2(0) [\cdots]
      Ama2(0)  
      Aba2† (11)  
mm2F     *Fmm2(0) Fdd2†(35)  
mm2I [\cdots] [\cdots] *Imm2(0) Iba2†(14)  
      Ima2(0)  
mmmP *Pmmm(0) Pccm(0) Pnnn(0) Pnna(1) Pbca(827)
  Pmma(0) Pban(0) Pcca(3)  
    Pmna(0) Pbam(0)  
    Pmmn(0) Pccn(37)  
      Pbcm(0)  
      Pnnm(0)  
      Pbcn(60)  
      Pnma(0)  
mmmC [\cdots] *Cmmm(0) Cmma(0) Cmcm(0) [\cdots]
      Cmca(0)  
      Cccm(0)  
      Ccca(0)  
mmmF [\cdots] [\cdots] *Fmmm(0) Fddd(2) [\cdots]
mmmI [\cdots] [\cdots] *Immm(0) Ibam(0)  
      Ibca(0)  
      Imma(0)  

(b) Tetragonal space groups. For *, † see Subsection 9.7.4.1[link].

Arithmetic crystal classFully symmorphicTending to symmorphismEqually balancedTending to antimorphismFully antimorphic
4P *P4(0) P42(1) [\cdots] [\cdots] P41,3(40)
4I [\cdots] [\cdots] I41(3) *I4(3) [\cdots]
[\overline {4}]P *P[\overline {4}](0) [\cdots] [\cdots] [\cdots] [\cdots]
[\overline {4}]I [\cdots] [\cdots] *I[\overline {4}](7) [\cdots] [\cdots]
4/mP *P4/m(0) P42/m(0) P4/n(1) P42/n(20) [\cdots] [\cdots]
4/mI [\cdots] [\cdots] [\cdots] *I4/m(0) I41/a†(29) [\cdots]
422P [\cdots] *P422(0) P4212(0) P41,3212†(49) [\cdots]
  P4222(0) P41,322(1) P42212(1)  
422I [\cdots] [\cdots] I4122†(0) *I422(0) [\cdots]
4mmP [\cdots] *P4mm(0) P4bm(0) P42cm(0) [\cdots]
      P42nm(0)  
      P4cc(0)  
      P4nc(0)  
      P42mc(0)  
      P42bc(1)  
4mmI [\cdots] [\cdots] [\cdots] *I4mm(0) [\cdots]
      I4cm(0)  
      I41md(0)  
      I41cd(5)  
[\overline {4}]2mP [\cdots] *P[\overline {4}]2m(0) P[\overline {4}]2c(0) P[\overline {4}]21c(12) [\cdots]
    P[\overline {4}]21m(0)    
[\overline {4}]m2P [\cdots] *P[\overline {4}]m2(0) P[\overline {4}]c2(0) [\cdots] [\cdots]
    P[\overline {4}]b2(0)    
    P[\overline {4}]n2(0)    
[\overline {4}]m2I [\cdots] [\cdots] *I[\overline {4}]m2(0) I[\overline {4}]c2†(0) [\cdots]
[\overline {4}]2mI [\cdots] [\cdots] *I[\overline {4}]2m(0) I[\overline {4}]2d(0) [\cdots]
4/mmmP [\cdots] *P4/mmm(0) P4/mcc(0) P4/nbm(0) [\cdots]
  P42/mmc(0) P4/nmm(0) P4/nnc(0)  
  P42/mcm(0)   P4/mbm(0)  
      P4/mnc(0)  
      P4/ncc(0)  
      P42/nbc(0)  
      P42/nnm(0)  
      P42/mbc(0)  
      P42/mnm(0)  
      P42/nmc(0)  
      P42/ncm(0)  
4/mmmI [\cdots] *I4/mmm(0) [\cdots] I4/mcm(0)  
      I41/amd(0)  
      I41/acd(0)  

(c) Trigonal space groups. For *, † see Subsection 9.7.4.1[link].

Arithmetic crystal classFully symmorphicTending to symmorphismEqually balancedTending to antimorphismFully antimorphic
3P *P3(0) [\cdots] [\cdots] [\cdots] P31,2(33)
3R [\cdots] [\cdots] [\cdots] *R3†(11) [\cdots]
[\overline {3}]P *P[\overline {3}](1) [\cdots] [\cdots] [\cdots] [\cdots]
[\overline {3}]R [\cdots] [\cdots] [\cdots] *R[\overline {3}](30) [\cdots]
312P 321P [\cdots] *P312(0) *P321(0) [\cdots] P31,212†(0) P31,221†(10) [\cdots]
32R [\cdots] [\cdots] [\cdots] *R32†(0) [\cdots]
3m1P 31mP [\cdots] *P3m1(0) *P31m(0) [\cdots] P3c1†(0) P31c(0) [\cdots]
3mR [\cdots] [\cdots] [\cdots] *R3m(0) R3c(7) [\cdots]
[\overline {3}]m1P [\overline {3}]1mP [\cdots] *P[\overline {3}]m1(0) *P[\overline {3}]1m(0) [\cdots] P[\overline {3}]c1†(0) P[\overline {3}]1c(0) [\cdots]
[\overline {3}]mR [\cdots] [\cdots] [\cdots] *R[\overline {3}]m(0) R[\overline {3}]c(0) [\cdots ]

(d) Hexagonal space groups. For *, † see Subsection 9.7.4.1[link].

Arithmetic crystal classFully symmorphicTending to symmorphismEqually balancedTending to antimorphismFully antimorphic
6P *P6(0) [\cdots] P62,4(1) P63(0) [\cdots] P61,5(22)
[\overline {6}]P *P[\overline {6}](0) [\cdots] [\cdots] [\cdots] [\cdots]
6/mP *P6/m(0) [\cdots] P63/m(0) [\cdots] [\cdots]
622P [\cdots] *P622(0) P62,422(0) [\cdots] P6322(1) P61,522†(2) [\cdots]
6mmP [\cdots] *P6mm(0) [\cdots] P6cc(0) [\cdots]
      P63cm(0) P63mc(0)  
[\overline {6}]m2P [\overline {6}]2mP [\cdots] *P[\overline {6}]m2(0) *P[\overline {6}]2m(0) [\cdots] P[\overline {6}]c2†(0) P[\overline {6}]2c(0)  
6/mmmP [\cdots] *P6/mmm(0) [\cdots] P6/mcc(0) [\cdots]
      P63/mcm(0) P63/mmc(0)  

(e) Cubic space groups. For *, †, see Subsection 9.7.4.1[link]. No examples with one molecule in general position were found, so the frequencies are omitted.

Arithmetic crystal classFully symmorphicTending to symmorphismEqually balancedTending to antimorphismAntimorphic except for 3
23P [\cdots] *P23 [\cdots] [\cdots] P213†
23F [\cdots] [\cdots] *F23† [\cdots] [\cdots]
23I [\cdots] [\cdots] *I23 I213† [\cdots] [\cdots]
m[\overline 3]P [\cdots] *Pm[\overline 3] Pn[\overline 3] [\cdots] Pa[\overline 3 ]
m[\overline 3]F [\cdots] [\cdots] *Fm[\overline 3] Fd[\overline 3] [\cdots]
m[\overline 3]I [\cdots] [\cdots] *Im[\overline 3] Ia[\overline 3] [\cdots]
432P [\cdots] *P432 [\cdots] P4232† P41,332† [\cdots]
432F [\cdots] [\cdots] *F432 F4132† [\cdots]
432I [\cdots] [\cdots] *I432 I4132† [\cdots]
[\overline {4}]3mP [\cdots] *P[\overline {4}]3m [\cdots] P[\overline {4}]3n [\cdots]
[\overline {4}]3mF [\cdots] [\cdots] *F[\overline {4}]3m F[\overline {4}]3c [\cdots]
[\overline {4}]3mI [\cdots] [\cdots] *I[\overline {4}]3m I[\overline {4}]3d [\cdots]
m[\overline {3}]mP [\cdots] *Pm[\overline {3}]m Pm[\overline {3}]n Pn[\overline {3}]m Pn[\overline {3}]n [\cdots]
m[\overline {3}]mF [\cdots] *Fm[\overline {3}]m [\cdots] Fm[\overline {3}]c Fd[\overline {3}]m Fd[\overline {3}]c
[m\overline {3}]mI [\cdots] *Im[\overline {3}]m [\cdots] Ia[\overline {3}]d [\cdots]