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How to show a group is a subgroup of A_14?
Posted:
Dec 21, 2007 10:25 AM


Greetings,
Problem: I want to show that a simple group G of order 4*3*7*13 must be isomorphic to a subgroup of A_14 (the alternating group of 14 letters).
Attempt: It is easy to show that there are 14 sylow 13subgroups. And so G act by conjugation on its sylow 7subgroups with a trivial kernel (since G is simple). This shows that G is a subgroup of S_14 (the symmetric group of 14 letters). What's the next step? Thanks in advance.



