Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×C32 ⋊ C4 |
| Sylow | C5 ⋊ #7473 |
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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=d,b^2=e,c^2=fg,e^2=fh,f^2=gh,g^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fg,g^a=gh,i^a=i^2,i^d=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084659);