Context :

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 _ { 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 } .

Conclusions :