Products of covering operations multiplication tables

It is usual to refer to the compound operation produced by applying two operations in succession as the product of the two operations. In order to investigate further whether the products of the known covering operations of the water molecule produce any new ones, it is helpful to construct a complete multiplication table, shown in the box. Each entry in the table gives the operation resulting from applying hrst the operation at the head of the column containing the entry, and then the operation at the left of the row. 

No new covering operations have been generated - perhaps we have already found all of them. 

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