<p>Males of the fruit fly <i>Drosophila melanogaster</i> produce sperm that are each, on average, a couple of millimetres long. Thousands of sperm are stored in a seminal vesicle of only about 200 µm in size. Although the evolutionary pressures underlying such extreme flagellar lengths have been investigated, the physical consequences of their gigantism remain unclear. Here we show that sperm are packed into a dense and highly aligned state. We also find that sperm exhibit system-wide collective material flows with persistent and slow-moving topological defects. Individual sperm, despite their extraordinary lengths and in contrast to their feeble motility in isolation, propagate rapidly through the flagellar material, moving in either direction along material director lines. To rationalize how these collective behaviours arise from the non-equilibrium dynamics of the constituents, we conceptualize the motion of individual sperm as topologically confined to a reptation-like tube formed by its neighbours. Here sperm advance through amplitude-constrained and internally driven bending waves, pushing off counterpropagating flagella. We derive a continuum theory that produces an extensile stress that can sustain an aligned flagellar material, and verify theoretical predictions. Our work suggests that active stresses in the flagellar material maintain the sperm unentangled in both male and female storage organs and establishes giant sperm in their native habitat as a physiologically relevant active matter system.</p>