Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#1572 ⋊ C2 |
| Sylow | C5 ⋊ #17812 |
602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=eg,e^2=g,f^2=h,b^a=be,e^a=eg,c^b=ch,d^c=dg,i^c=i^4,i^d=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 138701);