The 32 Classes of Symmetry

They are 10 elements of symmetry in crystals. These 10 symmetry operators can be combined in 32 ways to produce the 32 point groups tabulated in Table D.7. 

C Point group with a single n-fold rotation axis 

C Point group with a single vertical n-fold rotation axis, together with n vertical mirror plane 

Point group with an n-fold axis of rotary reflection 

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