AbelianGroup

AbelianGroup[{n1, n2, ...}] represents the direct product of the cyclic groups of degrees n1, n2, ....

Example

Define an abelian group and get its elements:

g = AbelianGroup[{2, 3}];
GroupElements[g]
(* {{0, 0}, {0, 1}, {0, 2}, {1, 0}, {1, 1}, {1, 2}} *)

Please visit the official Wolfram Language Reference for more details.