Space groups with no special Wyckoff positions (i.e. with no special crystallographic orbits) are called ﬁxed-point-free space groups or torsion-free space groups or Bieberbach groups. In ﬁxed-point-free space groups group every element other than the identity has infinite order.
Fixed-point-free space groups in E2
Only two ﬁxed-point-free space groups exist in E2: p1 and pg.
Fixed-point-free space groups in E3
Thirteen ﬁxed-point-free space groups exist in E3: P1, P21, Pc, Cc, P212121, Pca21, Pna21, P41, P43, P31, P32,P61, P65.
Section8.3.2 of the International Tablesof Crystallography, Volume A