For n different from 2, a group G of cohomological dimension n has an n-dimensional Eilenberg–MacLane space. It is also known that a group of cohomological dimension 2 has a 3-dimensional Eilenberg−MacLane space.
For n not equal to 2, a group G of cohomological dimension n has an n-dimensional Eilenberg–MacLane space. It is also known that a group with cohomological dimension 2 has a 3-dimensional Eilenberg–MacLane space.