Abstract
The article contains a classification of the groups indicated in the title, consisting of a parametrised list of groups, each relevant group being conjugate in GL(4,C) to precisely one group on the list (and each group on the list being relevant). Each group on this list is given by a generating set of matrices, whose entries are explicit functions of finitely many integers satisfying certain relations. Also included is a similar classification of the finite primitive subgroups of GL(2,C).
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