Four arithmetic non-equivalent metric tensor matrices,-have been derived in this paper according to a crystallographic general equation TN=T.T1,T3 and T4 are geometric equivalent ones,therefore,only T1 and T2 are geometric non-equivalent ones.Substituting T1 and T2 into NTN=T,two maximal finite groups can be derived, which have 48 and 24 elements respectively and belong to two crystallographic point groups.The other 30 point groups can be derived according to group-subgroup relationship.