There are several properties of rows which arise from group theory and can be useful in looking at properties of methods.
The order of a row is the number of times which that row has to be multiplied by itself before it gets back to rounds. For example, the row 21436587 has order 2, because if it is multiplied by itself twice, you get back to rounds. Similarly the row 23145678 has order 3, and the row 23456781 has order 8. This can be useful, for example, in seeing how many leads of a method are needed in a plain course before it comes round.
Another useful concept is the sign or parity of a row. A row is considered even if it takes an even number of swaps of pairs of bells to get from rounds to that row, and odd if it takes an odd number of swaps. (It can be shown that whether the number is odd or even doesn't depend on exactly what the sequence of swaps is).
Finally, every row can be expressed as a set of cycles. A cycle is a set of bells which move round in a sequential way as the row is repeated; for example, 21345678 has only one cycle, which is (12); and 12356478 has one cycle, which is (456). Combining these two cycles will give us the row 213564678.