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Character table of the simple group of order 168

Recall that a *simple* group is a non-trivial group *G* such that the only normal subgroups of *G* are {1} and *G* itself. We discussed briefly in Chapter 1 the significance of simple groups in the theory of finite groups. Examples of simple groups which we have met so far are cyclic groups of prime order, *A*_{5} and *A*_{6}. In fact the group *A*_{5}, of order 60, is the smallest non-abelian simple group. The next smallest is a certain group of order 168, and in this chapter we shall describe this group and find its character table. The group belongs to a whole family of simple groups, and we begin with a description of this family.

**Special linear groups**

Let *p* be a prime number, and recall that _{p} is the field which ...

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