abstract. given a finite group g and a faithful irreducible f g-module v where f has
prime order, does g have a regular orbit on v ? this problem is equivalent to determining
which primitive permutation groups of affine type have a base of size 2. we classify the
pairs (g, v ) for which g has no regular orbit on v , where g is a covering group of an
almost simple group whose socle is sporadic and v is a faithful irreducible f g-module
such that the order of f is prime and divides the order of g. for such (g, v ), we also
determine the minimal base size of g in its action on v .