Wikipedia says a bispinor is an element of a 4-dimensional complex vector space considered as a (½,0)⊕(0,½) representation of the Lorentz group. Georgi defines a group as a mapping $D$ from a group $G$ onto a set of linear operators such that
1. $D(e)=1$
2. $D(g_1)D(g_2)=D(g_1g_2)$