International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.5, p. 851

Table 3.5.4.2 

E. Kocha and W. Fischera

Table 3.5.4.2| top | pdf |
Normalizers of the three-dimensional point groups with respect to the full isometry group of the sphere

The upper part refers to the crystallographic, the lower part to the noncrystallographic point groups as listed in Table 3.2.1.6[link] . The letter n represents an arbitrary integer; (2n) represents an even number.

NormalizerPoint groups
[m\overline{\infty}] [1, \overline{1}]
[m\overline{3}m] [222, mmm, 23, m\overline{3}, 432, \overline{4}3m, m\overline{3}m]
[\infty/mm] [2, m, 2/m, 4, \overline{4}, 4/m, 3, \overline{3}, 6, \overline{6}, 6/m]
[12/mmm] [622, 6mm, 6/mmm]
[8/mmm] [422, 4mm, 4/mmm]
[6/mmm] [32, 3m, \overline{3}m, \overline{6}2m]
[4/mmm] [mm2, \overline{4}2m]
[m\overline{\infty}] [2\infty, m\overline{\infty}]
[m\overline{35}] [235, m\overline{35}]
[\infty/mm] [n, \overline{n}, n/m, \infty, \infty/m, \infty 2, \infty m, \infty/mm]
[(2n)/mmm] [n22, nmm, n/mmm, n2, nm, \overline{n}m]
[n/mmm] [\overline{n}2m]