Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×Q8⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #9666 |
534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=df,c^2=eg,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cgh,i^c=i^4176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 68477);