  The direct bandgap found in hexagonal germanium and some of its alloys with
silicon allows for an optically active material within the group-IV
semiconductor family with various potential technological applications.
However, there remain some unanswered questions regarding several aspects of
the band structiure, including the strength of the electric dipole transitions
at the center of the Brillouin zone. Using the $\mathbf{k\cdot p}$ method near
the $\Gamma$ point, including 10 bands, and taking spin-orbit coupling into
account, we obtain a self-consistent model that produces the correct band
curvatures, with previously unknown inverse effective mass parameters, to
describe 2H-Ge via fitting to {\it ab initio} data and to calculate effective
masses for electrons and holes. To understand the weak dipole coupling between
the lowest conduction band and the top valance band, we start from a spinless
12-band model and show that when adding spin-orbit coupling, the lowest
conduction band hybridizes with a higher-lying conduction band, which cannot be
explained by the spinful 10-band model. With the help of L\"owdin's
partitioning, we derive the effective low-energy Hamiltonian for the conduction
bands for the possible spin dynamics and nanostructure studies and in a similar
manner, we give the best fit parameters for the valance-band-only model that
can be used in the transport studies. Finally, using the self-consistent
10-band model, we include the effects of a magnetic field and predict the
electron and hole g-factor of the conduction and valance bands.
