Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #8561 |
678 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=d,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^2,c^b=ch,i^b=i^4,f^c=fg,i^f=i^492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1088388);