  Aims. We aim to probe the internal structure and investigate more detailed
information of the $\delta$ Scuti star HD 50844 with asteroseismology. Methods.
We analyse the observed frequencies of the $\delta$ Scuti star HD 50844
obtained by Balona (2014), and search for possible multiplets based on the
rotational splitting law of g-mode. We tried to disentangle the frequency
spectra of HD 50844 by means of the rotational splitting only. We then compare
them with theoretical pulsation modes, which correspond to stellar evolutionary
models with various sets of initial metallicity and stellar mass, to find the
best-fitting model. Results. There are three multiplets including two complete
triplets and one incomplete quintuplet, in which mode identifications for
spherical harmonic degree $l$ and azimuthal number $m$ are unique. The
corresponding rotational period of HD 50844 is found to be
2.44$^{+0.13}_{-0.08}$ days. The physical parameters of HD 50844 are well
limited in a small region by three modes identified as nonradial ones
($f_{11}$, $f_{22}$, and $f_{29}$) and by the fundamental radial mode
($f_{4}$). Our results show that the three nonradial modes ($f_{11}$, $f_{22}$,
and $f_{29}$) are all mixed modes, which mainly represent the property of the
helium core. The fundamental radial mode ($f_{4}$) mainly represents the
property of the stellar envelope. In order to fit these four pulsation modes,
both the helium core and the stellar envelope must be matched to the actual
structure of HD 50844. Finally, the mass of the helium core of HD 50844 is
estimated to be 0.173 $\pm$ 0.004 $M_{\odot}$ for the first time. The physical
parameters of HD 50844 are determined to be $M=$ 1.81 $\pm$ 0.01 $M_{\odot}$,
$Z=$ 0.008 $\pm$ 0.001. $T_{\rm eff}=$ 7508 $\pm$ 125 K, log$g=$ 3.658 $\pm$
0.004, $R=$ 3.300 $\pm$ 0.023 $R_{\odot}$, $L=$ 30.98 $\pm$ 2.39 $L_{\odot}$.
