In the mathematical area of group theory, the covering groups of the alternating and symmetric groups are groups that are used to understand the projective representations of the alternating and symmetric groups. The covering groups were classified in: for n ≥ 4, the covering groups are 2-fold covers except for the alternating groups of degree 6 and 7 where the covers are 6-fold. For example the binary icosahedral group covers the icosahedral group, an alternating group of degree 5, and the binary tetrahedral group covers the tetrahedral group, an alternating group of degree 4.
