t =: ...
table =: 20 20 $ t
transposed =: >  table ; (|: table) ; ([  /. table) ; ([  /. |. table)
cycles =: 0 ,"1 (0 ,"0 i. 20)
foursomes =: 4 {."1 cycles |. transposed
>./ , */"1 foursomes

Or better

table =: 20 20 $ ...
transposed =: (] ` |: ` ([  /.) ` ([ /.@|.)) `:0 table
>./ , 4 */\"1 transposed