Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#1397 ⋊ C2 |
| Sylow | C5 ⋊ C4×M64 |
250 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 147 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=d,b^2=e,d^2=f,f^2=g,g^2=h,c^a=ch,i^b=i^4,i^c=i^4320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89744);