Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C16 ⋊ C2 |
| Sylow | C5 ⋊ #13476 |
382 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=de,b^2=dgh,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,i^a=i^4,c^b=cf,d^c=dg,e^c=egh,f^c=fgh,g^c=gh,i^c=i^4212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89334);