Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#529 ⋊ C4 |
| Sylow | C5 ⋊ #17546 |
1194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,c^2=g,d^2=gh,e^2=h,b^a=be,c^a=cg,e^a=eg,i^a=i^2,e^b=eh,f^b=fgh,i^c=i^4,i^f=i^492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1100540);