Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C5×C4⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ #34216 |
2422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=gh,c^2=g,d^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^d=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 330031);