On 2-arc-transitive representations of the groups of fourth-power-free order

A complete classification of 2-arc-transitive representations of primitive or bi-primitive groups of fourth-power-free order is given. The list consists of the following graphs: K"n, K"n","n-nK"2, K"r","r with r an odd prime, Peterson graph O"2, incidence and non-incidence graphs HD(11,5,2) and HD(11,6,2) of the Hadamard design on 11 points, some explicit coset graphs of two-dimensional projective groups PSL(2,p^l) with 1@?l@?2 and of Janko simple group J"1, and the standard double cover of these coset graphs. Moreover, a classification of primitive permutation groups of fourth-power-free order is given.