According to behavioural ecology theory, sociality evolves when the benefits of close association with conspecifics exceed the costs. Still, even when sociality evolves, the balance between costs and benefits differentiates amongst individuals in a group where each individual is selected to maximize its own fitness. In this study we aim to find correlations between fitness and social interactions and activity, and to test whether one of the prevailing social behaviour models, dominance hierarchy and self-organization, can describe social behaviour in a large group of grazing cows. Direct observations and drone video recordings were carried out in a herd of 130 ± 12 cows during two consecutive summers in a typical Mediterranean pasture in northern Israel. Observations' frequency was two to three weekly, lasting 4 ± 2 h each, during resting, grazing and feeding times. Agonistic interactions, allogrooming and grouping were recorded. Locomotion activity was monitored continuously by electronic pedometers. We calculated dominance probability, using the "Percolation and conductance" network approach whereby multiple indirect dominance pathways in the network are used to fill in missing data in the win/loss matrix. Dominance probability calculated was ambiguous (inconsistent dominance direction) with resulting average dominance index of 0.56 ± 0.029. Proxies for fitness were calving-to-conception interval and calf weaning weight. Calves were not considered as part of the group. Multiple regression analyses showed a positive effect of grouping and negative effect of oscillating grazing activity pattern on fitness response (p = 0.012; p = 0.01 for calving to conception interval and weaning weight respectively). Oscillating activity pattern was expressed in high Coefficient of Variance value of stepping activity. We suggest that in a large group of free grazing beef cows, social organization does not result from dominance hierarchy, and is better described by self-organizing systems hypothesis. Herd schedule and activity patterns were repetitive, but individuals' schedule within it was not. Individuals' morning grazing activity patterns were repetitive, but other daily hours' activity was not and individuals' nearest neighbours were changing continuously between daily activity sessions.