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We demonstrate an economic and concise method for representingthe elements of groups involved in the Suzuki chain. For example,we represent each element of Suz:2 by a permutation on 14letters from L3(2):2 followed by four words, each of length atmost two, in 14, 36, 100, and 416 involutory symmetricgenerators, respectively. Such expressions will have an obviousadvantage over permutations on 1782 provided that it isreasonably simple to multiply and invert them. We refer to thisas nested symmetric representation of an element of thegroup

Nested symmetric representation of elements of the Suzuki chain groups