Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #12819 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=d,c^2=h,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^4,e^c=egh,f^c=fh,g^c=gh158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 85649);