Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#1839 ⋊ C2 |
| Sylow | C5 ⋊ #20772 |
1062 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 299 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=ef,c^2=e,g^2=h,b^a=be,c^a=cf,d^a=dh,i^d=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 169816);