Question: How to restore the PermutationGroup from its output

After this code:

g1 := PermutationGroup({[[1, 2]], [[1, 2, 3], [4, 5]]})

g1:=<(1, 2), (1, 2, 3)(4, 5)>

I can get a string "<(1, 2), (1, 2, 3)(4, 5)>". Could I use the string to restore the PermutationGroup with an elegant method?

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