Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#1303 ⋊ C2 |
| Sylow | C5 ⋊ #10372 |
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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=dh,e^2=gh,f^2=g,b^a=bd,c^a=ce,e^a=eh,c^b=cf,e^b=eg,i^b=i^4,d^c=dg,e^c=egh,f^c=fg,i^c=i^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 72705);