When interpreted as quaternions, the 120 vertices of the 600-cell form a group under quaternionic multiplication. This group is often called the binary icosahedral group and denoted by "2I" as it is the double cover of the ordinary icosahedral group "I". It occurs twice in the rotational symmetry group "RSG" of the 600-cell as an invariant subgroup, namely as the subgroup "2IL" of quaternion left-multiplications and as the subgroup "2IR" of quaternion right-multiplications. Each rotational symmetry of the 600-cell is generated by specific elements of "2IL" and "2IR"; the pair of opposite elements generate the same element of "RSG". The centre of "RSG" consists of the non-rotation "Id" and the central inversion "−Id". We have the isomorphism "RSG ≅ (2IL × 2IR) / {Id, -Id}". The order of "RSG" equals = 7200.