Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#1460 ⋊ C2 |
| Sylow | C5 ⋊ #8397 |
802 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 127 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=f,b^2=gh,c^2=h,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,f^b=fgh,i^b=i^4,f^c=fg131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 61339);