Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #10596 |
386 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=deh,b^2=d,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,i^b=i^4,d^c=dg,e^c=eh,f^c=fg,i^c=i^4122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 74145);