Direct products of k simple groups with abelian Sylow 2-subgroups can be spectrum-unique for arbitrary k, while the cube of ^2G_2(q) and fourth power of J_1 each have infinitely many isospectral groups.
Ree, A family of simple groups associated with the simple Lie alge bra of type (G2), Amer
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On finite groups isospectral to groups with abelian Sylow $2$-subgroups
Direct products of k simple groups with abelian Sylow 2-subgroups can be spectrum-unique for arbitrary k, while the cube of ^2G_2(q) and fourth power of J_1 each have infinitely many isospectral groups.