Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#1290 ⋊ C2 |
| Sylow | C5 ⋊ #7986 |
546 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=g,d^2=gh,e^2=g,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,e^b=eh,i^c=i^4128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 59461);