Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#2115 ⋊ C2 |
| Sylow | C5 ⋊ #12685 |
890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 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,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^4,d^b=dh,e^b=eh,f^b=fh,i^b=i^4,d^c=dh152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 85022);