Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#3407 ⋊ C2 |
| Sylow | C5 ⋊ #33388 |
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,e^2=g,g^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^4,e^b=egh,f^b=fh,g^b=gh,i^b=i^4,d^c=dh194 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 322516);