Context : The Abell 780 cluster , better known as the Hydra A cluster , has been thouroughly analyzed in X-rays .
However , little is known on its optical properties .

Aims : We propose to derive the galaxy luminosity function ( GLF ) in this apparently relaxed cluster , and to search for possible environmental effects by comparing the GLFs in various regions , and by looking at the galaxy distribution at large scale around Abell 780 .

Methods : Our study is based on optical images obtained with the ESO 2.2m telescope and WFI camera in the B and R bands , covering a total region of 67.22 \times 32.94 arcmin ^ { 2 } , or 4.235 \times 2.075 Mpc ^ { 2 } for a cluster redshift of 0.0539 .

Results : In a region of 500 kpc radius around the cluster centre , the GLF in the R band shows a double structure , with a broad and flat bright part and a flat faint end that can be fit by a power law with an index \alpha \sim - 0.85 \pm 0.12 in the 20.25 \leq R \leq 21.75 interval .
If we divide this 500 kpc radius region in North+South or East+West halves , we find no clear difference between the GLFs in these smaller regions .
No obvious large scale structure is apparent within 5 Mpc from the cluster , based on galaxy redshifts and magnitudes collected from the NED database in a much larger region than that covered by our data , suggesting that there is no major infall of material in any preferential direction .
However , the Serna-Gerbal method reveals the presence of a gravitationally bound structure of 27 galaxies , which includes the cD , and of a more strongly gravitationally bound structure of 14 galaxies .

Conclusions : These optical results agree with the overall relaxed structure of Abell 780 previously derived from X-ray analyses .