ClassRootsCharTable( tbl )
returns a list of the classes of all nontrivial p--th roots of the classes of tbl where for each class, p runs over the prime divisors of the representative order.
gap> ClassRootsCharTable(L3_2); [ [ 2, 3, 5, 6 ], [ 4 ], [ ], [ ], [ ], [ ] ]
This information is found by looking at the powermap of tbl, too.
GAP 3.4.4