The author constructs the triple cover 3.O’N of the O’Nan group as the automorphism group of a certain totally skew trilinear form on a 45- dimensional vector space over GF(7). Let \(\Omega\) be a set of 11 elements on which the Mathieu group \(M_{11}\) acts naturally. Let \(\Omega_{10}\) be the vector space over GF(7) spanned by 11 vectors \(\omega_ i\), \(i\in \Omega\), with \(\sum_{i}\omega_ i=0\) and let \(V=\wedge\) \(2\Omega_{10}\) be the 2-fold exterior power. Then V is spanned by \(v_{ij}=\omega_ i\wedge \omega_ j\) for \(i\neq j\) with the relations \(v_{ij}=-v_{ji}\) and \(\sum_{i}v_{ij}=0\) for each j. A totally skew trilinear form on V is a trilinear form [,, ] such that \([u,v,w]=- [v,u,w]=[v,w,u]\) for any choices of u, v, w in V. The author defines explicitly an \(M_{11}\)-invariant totally skew trilinear form on V and shows that the subgroup G of GL(V) which leaves the form invariant is isomorphic to 3.O’N. The identification of G with 3.O’N is accomplished by studying a Sylow 2-subgroup of G. The author also defines an algebra structure on \(U=V\oplus W\), where V and W are dual to each other as 3.O’N-modules and interchanged by the outer automorphism. The module U provides a 90-dimensional irreducible representation of the group 3.O’N:2 in the notation of [“ATLAS of Finite Groups”, Oxford, Clarendon Press (1985; Zbl 0568.20001)]. This paper contains much information about the structure of the O’Nan group. The presentation of 3.O’N obtained here is useful for the study of the group.