1. The problem statement, all variables and given/known data I need to find a group with twelve elements that is noncommutative. 2. Relevant equations 3. The attempt at a solution I was considering a group G of the integers (-5,-4,-3,-2-,-1,0,1,2,3,4,5) with respect to subtraction. Subtraction is associative/noncommutative, G has the neutral element, and every element has an inverse! Excellent! But (!) it composes only eleven elements! I need twelve!