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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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27

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, A5 and A6. In fact the group A5, 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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