What is the order of permutation in $S_6$ of: $(1 2) \circ (152) \circ (1634) \circ(125)$
2026-03-27 07:18:47.1774595927
Calculate the order of permutation of cycle compositions
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Your decomposition is not correct. You should obtain $$(1\,2)(1\,5)(1\,6\,3\,4)(1\,2\,5)=(3\,4\,5\,6),$$ so the order is the length ($4$) of this cycle.
Edit: with the last modification of the permutation, we have $$(1\,2)(1\,5\,2)(1\,6\,3\,4)(1\,2\,5)=(1\,2)(3\,4\,5\,6)$$ so its order of this product is the l.c.m. of the lengths of the disjoint factors, which is again $4$.