Find the order of the subgroup of the symmetric group s6 gen

Find the order of the subgroup of the symmetric group s_6 generated by the complex {(1234), (14)(32), (56)}

Solution

we known that order of cycle (a,b.c)(d,e)

how to find order

that is order=lcm(3,2)=6

by this we find order of subgroup genrated by {(1234),(14)(32),(56)}

oeder 0f subgroup=lcm{4,lcm(2,2),2}

=lcm(4,2,2)

=4

therfore order of subgroup of symmetric group s₆ genrated by {(1234),(14)(32),(56)}is 4