Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C5×#518 ⋊ C4 |
| Sylow | C5 ⋊ #20354 |
2410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,b^a=be,e^a=eh,f^b=fh,i^b=i^2,d^c=dh,i^g=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #72253755, #72253757, #72269813, … |
| maximal normal subgroup of | #72253755, #72253757, #72269813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1103457);