Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×C8×D4 ⋊ C4 |
| Sylow | C5 ⋊ #8202 |
570 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=e,d^2=g,e^2=h,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=ch,i^b=i^2,i^f=i^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1087238);