  Nonunitary superconductivity has attracted renewed interest as a novel
gapless phase of matter. In this study, we investigate the superconducting gap
structure of nonunitary odd-parity chiral pairing states in a superconductor
involving strong spin-orbit interactions. By applying a group theoretical
classification of chiral states in terms of discrete rotation symmetry, we
categorized all possible point-nodal gap structures in nonunitary chiral states
into four types in terms of the topological number of nodes and node positions
relative to the rotation axis. In addition to conventional Dirac and Weyl point
nodes, we identify a novel type of Dirac point node unique to nonunitary chiral
superconducting states. The node type can be identified experimentally based on
the temperature dependence of the nuclear magnetic resonance longitudinal
relaxation rate. The implication of our results for a nonunitary odd-parity
superconductor in UTe$_2$ is also discussed.
