A microscopic approach based on the algebraic version of the resonating group method was implemented by applying it to the radiative capture reaction 3He(α, γ)7Be. The astrophysical S-factor of the reaction and the branching ratio between the capture to the ground and the first excited states of the 7Be nucleus were calculated. A comparison of the theoretical results with the most recent experimental data was performed, and good agreement with these data was found. Advantages of the theoretical approach realized are indicated, and possible ways to refine upon it are outlined.