Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C5×#553 ⋊ C4 |
| Sylow | C5 ⋊ #34319 |
2344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=fg,c^2=fg,d^2=f,e^2=h,b^a=bf,c^a=cg,e^a=ef,i^a=i^3,d^b=df,i^e=i^2,i^h=i^4113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114430);