Flag‐transitive 2‐ designs of product type

In this paper, we prove that if a 2‐ design admits a flag‐transitive automorphism group G, then G is of affine, almost simple type, or product type. Furthermore, we prove that if G is product type then is either a 2‐(25, 4, 12) design or a 2‐(25, 4, 18) design with .