  Anomalous Hall effect (AHE), one of the most important electronic transport
phenomena, generally appears in ferromagnetic materials but is rare in
materials without magnetic elements. Here, we present a study of
La$_3$MgBi$_5$, whose band structure carries multitype Dirac fermions. Although
magnetic elements are absent in La$_3$MgBi$_5$, clear signals of AHE can be
observed. In particular, the anomalous Hall conductivity is extremely large,
reaching 42,356 $\Omega^{-1}$ cm$^{-1}$ with an anomalous Hall angle of 8.8 %,
the largest one that has been observed in the current AHE systems. The AHE is
suggested to originate from the combination of skew scattering and Berry
curvature. Another unique property discovered in La$_3$MgBi$_5$ is the axial
diamagnetism. The diamagnetism is significantly enhanced and dominates the
magnetization in the axial directions, which is the result of restricted motion
of the Dirac fermion at Fermi level. Our findings not only establish
La$_3$MgBi$_5$ as a suitable platform to study AHE and quantum transport, but
also indicate the great potential of 315-type Bi-based materials for exploring
novel physical properties.
