Are analyzed experimental data on fluorescence DNA complexes inside neutrophils and other cells in flow cytometry experiments with nanometer spatial resolution in the large populations of cells. It is shown that DNA information is packed in ultra dense fractal networks of 'exponentially small worlds'. The exponential growth of high order's central moments for fluctuations information in DNA fluorescence characterizes existence of intermittency in joint information complexes DNA inside living cell. Intermittency selects and ensures dominating role of corresponding correlations in DNA information. Intermittency depends on the correlation scales and order of chromosomal correlations (cooperative links). Intermittency of DNA information occurs in the coalitions of chromosomes and exists if number of correlated DNA is not small and more than one, two or three; this is the collective effect. Intermittency is observed for different, rather high orders of multiple chromosomal correlations and depends on a personal health status in given time. Strong or weak level of intermittency in information activity of correlated chromosomes also depends on the health conditions. All these facts reflect various distributions of high order's central moments for fluctuations in DNA information; oscillations, growth, decrease, switching of various functions at changes the scale, number or order of chromosomal correlations. Intermittency defines the basic natural properties of DNA activity inside cells and DNA chips.