Difference between oxidation number and group number?
Group number is just the number of column in the periodic table in which the element is located (the most common numbering is 18-group (IUPAC).
Oxidation number is nominal and describes the degree of loss of electrons for an element in a particular compound; is is an integer that corresponds to the number of lost/gained electrons. It has positive sign if electrons were lost or negative sign if electrons were gained (assuming the complete transfer of electrons to the more electronegative atom). For some elements it can be different depending on the compound. Oxidation number is always zero for all pure elements.