| 
        
          
            | 
 | List
of superperfect groups 
 
 
 | 
 |  
            | Order 
 | Perfect
Group
Number 
 | Third
integral
homology 
 |  
            | 
 | 
 | 
 |  
            | 120 
 | 1 
 | [ 8, 3, 5 ] 
 |  
            | 336 
 | 1 
 | [16,3] 
 |  
            | 504 
 | 1 
 | [
2, 9, 7 ] 
 |  
            | 1320 
 | 1 
 | [
8, 3, 5 ] 
 |  
            | 2160 
 | 1 
 | [
16, 3, 3, 5 ] 
 |  
            | 2184 
 | 1 
 | [
8, 3, 7 ] 
 |  
            | 2688 
 | 3 
 | [
8, 8, 3 ] 
 |  
            | 3840 
 | 6 
 | ??? 
 |  
            | 3840 
 | 7 
 | ??? 
 |  
            | 4080 
 | 1 
 | [
3, 5, 17 ] 
 |  
            | 4896 
 | 1 
 | [
32, 9 ] 
 |  
            | 5376 
 | 1 
 | ??? 
 |  
            | 5616 
 | 1 
 | [
8, 3 ] 
 |  
            | 6048 
 | 1 
 | [
8, 9, 5 ] 
 |  
            | 7920 
 | 1 
 | [
8 ] 
 |  
            | 9720 
 | 2 
 | [
8, 9, 5 ] 
 |  
            | 12144 
 | 1 
 | [
16, 3, 11 ] 
 |  
            | 14400 
 | 1 
 | [
8, 8, 3, 3, 5, 5 ] 
 |  
            | 15000 
 | 2 
 | [
8, 3, 5, 25 ] 
 |  
            | 15000 
 | 3 
 | ??? 
 |  
            | 15120 
 | 1 
 | [
16, 3, 3 ] 
 |  
            | 15360 
 | 4,6-7:
Not
yet checked if these are superperfect 
 | 
 |  
            | 15600 
 | 1 
 | [
16, 3, 13 ] 
 |  
            | 19656 
 | 1 
 | [
8, 3, 7, 13 ] 
 |  
            | 21504 
 | 5-22:
Not
yet checked if these are superferfect 
 | 
 |  
            | 24360 
 | 1 
 | [
8, 3, 5, 7 ] 
 |  
            | 29160 
 | 1 
 | ??? 
 |  
            | 29160 
 | 3:
Not yet checked if this is superperfect 
 | 
 |  
            | 29760 
 | 1 
 | [
64, 3, 5 ] 
 |  
            | 32256 
 | 1-2: Not yet checked if these are
superperfect 
 | 
 |  
            | 32736 
 | 1 
 | [ 3,
11, 31 ] 
 |  
            | 34560 
 | 4 
 | ??? 
 |  
            | 37500 
 | 1:
Not yet checked if this is superperfect 
 | 
 |  
            | 40320 
 | 1 
 | [ 8,
16, 3, 3, 5 ] 
 |  
            | 40320 
 | 3 
 | ??? 
 |  
            | 43008 
 | 1-25:
Not yet checked if these are superperfect 
 | 
 |  
            | 46080 
 | 1:
Not yet checked if this is superperfect 
 | 
 |  
            | 50616 
 | 1 
 | [ 8,
9, 19 ] 
 |  
            | 51840 
 | 1 
 | ??? 
 |  
            | 57624 
 | 1-2:
Not yet checked if these are superperfect 
 | 
 |  
            | 58320 
 | 2:
Not yet checked if this is superperfect 
 | 
 |  
            | 62400 
 | 1 
 | ??? 
 |  
            | 64512 
 | 1-4:
Not yet checked if these are superperfect 
 | 
 |  
            | 68880 
 | 1 
 | [ 16,
3, 5, 7 ] 
 |  
 |