Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C5 ⋊ #20451 |
1142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=ef,d^2=h,e^2=h,f^2=h,b^a=be,c^a=ch,e^b=eh,f^b=fh,i^c=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 167628);