M
          
          
            22
          
        
      
    
    {\displaystyle \mathrm {M} _{22}}
   has the first five prime numbers as its distinct prime factors in its order of 27·32·5·7·11, and is the smallest of five sporadic groups with five distinct prime factors in their order.
These are also the first five sporadic groups to have been described, defined as 
  
    
      
        
          
            M
          
          
            n
          
        
      
    
    {\displaystyle \mathrm {M} _{n}}
   multiply transitive permutation groups on 
  
    
      
        n
      
    
    {\displaystyle n}
   objects, with 
  
    
      
        n
      
    
    {\displaystyle n}
   ∈ {11, 12, 22, 23, 24}.