Classification and properties (12,5)-configurations

The combinatorial objects — $(v,k)$-configurations are studied for $k=5$. All $(12,5)$-configurations constructed by 2-orgraphs with 6 vertices and by groups of order 12 are described. The number of combinatorially non-equivalent $(12,5)$-configurations is computed, new examples of $(12,5)$-configurations are provided. Some properties of $(12,5)$-configurations are studied: a set of vertex types and a group of automorphisms. An algorithm for constructing an automorphism group of an arbitrary $(v,5)$-configuration is developed. A theorem on the structure of the automorphism group for $(v,5)$ configurations from some series is proved.