Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #9680 |
826 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=dfg,c^2=e,d^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^4,d^b=dh,f^b=fh218 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 68550);