For every integer m >= 1, there is a connected tetravalent half-arc-transitive graph with vertex stabilizer D8^2 x C2^m, built as a coset graph on the alternating group A_{2m+6}.
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Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers
For every integer m >= 1, there is a connected tetravalent half-arc-transitive graph with vertex stabilizer D8^2 x C2^m, built as a coset graph on the alternating group A_{2m+6}.