Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#547 ⋊ C4 |
| Sylow | C5 ⋊ #8428 |
1020 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,d^2=h,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,d^b=dh,f^b=fgh,i^b=i^4,e^c=eg,f^c=fg,i^f=i^468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1088039);