Exact charged and rotating toroidal black hole in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:m

In this paper, we construct an exact solution of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:math> Einstein-Skyrme model in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mo>=</e:mo><e:mn>4</e:mn></e:math> space-time dimensions describing a charged and rotating black hole with toroidal horizon. Rotation is added by applying an improper coordinate transformation to the known static toroidal black hole with Skyrme hair, while the electric charge is supplemented by considering a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:mo stretchy="false">)</g:mo></g:math> gauge field interacting with Einstein gravity. We perform the thermal analysis in the grand canonical ensemble, explicitly showing the role that the flavor number plays. Some discussions about stability are also considered.