The noncentrosymmetric ferromagnet Cr11Ge19 has been investigated by electrical transport, AC and DC magnetization, heat capacity, x-ray diffraction, resonant ultrasound spectroscopy, and first principles electronic structure calculations. Complex itinerant ferromagnetism in this material is indicated by nonlinearity in conventional Arrott plots, unusual behavior of AC susceptibility, and a weak heat capacity anomaly near the Curie temperature (88 K). The inclusion of spin wave excitations was found to be important in modeling the low temperature heat capacity. The temperature dependence of the elastic moduli and lattice constants, including negative thermal expansion along the c axis at low temperatures, indicates strong magneto-elastic coupling in this system. Calculations show strong evidence for itinerant ferromagnetism and suggest a noncollinear ground state may be expected.