Roger Penrose wrote in "The Road to Reality" that the symmetry to describe the weak force is the "group SU(2) x U(1) or more correctly, U(2)". (page 641) And "The group might be expressed as SU(2) x U(1)/Z2, where the '/Z2' means 'factor out by a Z2 subgroup'. However, there is more than one such subgroup, so this notation is not fully explicit. The notation 'U(2)' automatically picks out the correct one." (page 654) I like to understand what the group U(2) is. The group U(1) corresponds to the circle group. wiki: "U(1) is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane." But to what corresponds the group U(2)?