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Dominant individuals are often most influential in their social groups, affecting movement, opinion, and performance across species and contexts. Yet, behavioral traits like aggression, intimidation, and coercion, which are associated with and in many cases define dominance, can be socially aversive. The traits that make dominant individuals influential in one context may therefore reduce their influence in other contexts. Here, we examine this association between dominance and influence using the cichlid fish Astatotilapia burtoni, comparing the influence of dominant and subordinate males during normal social interactions and in a more complex group consensus association task. We find that phenotypically dominant males are aggressive, socially central, and that these males have a strong influence over normal group movement, whereas subordinate males are passive, socially peripheral, and have little influence over normal movement. However, subordinate males have the greatest influence in generating group consensus during the association task. Dominant males are spatially distant and have lower signal-to-noise ratios of informative behavior in the association task, potentially interfering with their ability to generate group consensus. In contrast, subordinate males are physically close to other group members, have a high signal-to-noise ratio of informative behavior, and equivalent visual connectedness to their group as dominant males. The behavioral traits that define effective social influence are thus highly context specific and can be dissociated with social dominance. Thus, processes of hierarchical ascension in which the most aggressive, competitive, or coercive individuals rise to positions of dominance may be counterproductive in contexts where group performance is prioritized.