Hermann-Mauguin crystal group symbols

Note. The Hermann-Mauguin space group notation for any particular crystal comprises two parts. The first part identifies the Bravais lattice type into which the crystal belongs and the second part identifies the total symmetry of the array of atoms in the crystal and therefore also the crystal system. In the second part that identifies the symmetry, only those symmetry elements are included in the symbol that are necessary to describe the space group uniquely. The remainders are being omitted since they follow, as a necessary consequence. 

Table 2.4. Space groups, crystal systems, point groups, and the Hermann-Mauguin Symbols.

Any solid object can be classified in terms of the collection of symmetry elements that can be attributed to the shape. The combinations of allowed symmetry elements form the general three-dimensional point groups or non-crystal-lographic three-dimensional point groups. The symmetry operators are described here by the International or Hermann-Mauguin symbols. 

Point group number Hermann-Mauguin symbol Crystal system Centrosymmetric Polar Sohncke group... 

---