Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C5×#416 ⋊ C2 |
| Sylow | C5 ⋊ #60366 |
4782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|e^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,i^a=i^4,f^b=fh,i^b=i^4,d^c=dh,i^c=i^4176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036043);