Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C22×C5×C22⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ #36719 |
2490 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=f,d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^4,c^b=ch,d^b=dfh164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 376560);