Generalized translation and axial point group:  G = T̂ ∘ P

Generalized translational group T̂:  product of two of the following 4 infinite cyclic groups

2D Generalized translational groups T̂:  product of two 1D generalized translational groups

 T T(a) ⊗T(b)1,2,3,4,6,8,10,11,13,14,18,19,22,23,26,27,35,37,47,49,50,51,53,55,57,59,61,65--80
 Th T(a) ⊗ Th(b) 5,7,31,38,41
 T(a) ⊗Th(½(a+b))2,34,36,39,42,46,48,52,62,64
 Tv  T(a) ∧ Tv(b) 12,16,24,30,40
 T(a) ∧Tv(½(a+b))56,58,63
 TU  T(a) ∧ TU(b) 9,15,20,28,29
 T(a) ∧TU(½(a+b)) 54,60
 TUh  TU(a) ∘Th(b) 33,43,45
 TUv  TU(a) ∘ Tv(b) 17
 TUU  TU(a) ∘ TU(b) 21
 Tvv  Tv(a) ∘ Tv(b) 25,44

Axial point group P:  one of the groups from the following 7 families for n=1,2,3,4,6