对称群S_5的特征性质

通过计算机计算，作者获得了S5的下列重要特征性质：①S5的子群的阶是：1，2，3，4，5，6，8，10，12，20，24，60，120；②S5共有156个子群，每个子群的构造均已清楚；③S5有19个共轭子群类，一个非平凡正规子群；④S5中各阶子群的个数，各共轭类中所含于群的个数均已清楚．

CONJUGATE GLASSES OF SUBGROUP IN PERMUTATION GROUPS S_5 AND PROGRAPH

To some problem in the finite group, with the gelping of the computer, we can do somevesearch by the method of calculation. If we discuss them only through the theorvy of group, we can seethat it is troublesome even it is very difficult. But if we design prgram and calculate with the computer,wecan obtain some good result. The characterization of S5 is obtained through the method of calculation themain result is described as the following:1) There are one hudread and fifty--six sulgroups of S5;2) There are nineteen conjugate classes of subgroup in S5.