A two-generated finite group has a planar generating graph if and only if it is one of C2, C3, C4, C5, C6, C2×C2, D3, D4, Q8, C4×C2, or D6.
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Finite groups with planar generating graph
A two-generated finite group has a planar generating graph if and only if it is one of C2, C3, C4, C5, C6, C2×C2, D3, D4, Q8, C4×C2, or D6.