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I'm referring to this post:

Unique minimal normal subgroup $\implies$ faithful irreducible representation.

Isn't the claim, that there is always a faithful irreducible representation (if $char(K) \nmid |G|$) trivial, because the trivial representation is always irreducible and faithful? So there whould be no need to look first, if there is an unique minimal normal subgroup.

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The trivial representation is not faithful unless $G$ is trivial. –  Clive Newstead Aug 2 '12 at 10:45
Oh, of course, everything goes to 1! –  Khanna Aug 2 '12 at 10:50

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