Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#432 ⋊ C4 |
| Sylow | C5 ⋊ #7868 |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,d^2=g,e^2=h,b^a=bd,c^a=ch,d^a=dg,f^a=fg,c^b=cg,i^b=i^2,i^c=i^4,i^f=i^492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1085626);