Determine the centralizer and the order of the conjugacy:
1) Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl_{2}(F_{3}).
2) Prove that the icosahedral group has a subgroup of order 10.
3) Let G be a group of order n which acts nontrivially on a set of order r. Prove that if n>r!, then G has a proper normal subgroup.
4) Determine the conjugacy classes in the dihedral group D_{10} and write down the class equation for this group. Find the center of D_{10}.