Germany's private sector recorded its strongest growth in nearly two-and-a-half years in October, buoyed by a robust rise in services activity, a survey showed on Friday. The HCOB preliminary German flash composite Purchasing Managers' Index, compiled by S&P Global, rose to 53.8 in October from 52.0 in September, marking the fastest growth since May 2023 and surpassing analysts' expectations of 51.5. October marks the fifth month in a row that the composite index, which tracks the services and manufacturing sectors that together account for more than two-thirds of the euro zone's largest economy, was above the 50 mark indicating growth.