Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C5×AΣL(1,𝔽16) ⋊ C4 |
| Sylow | C5 ⋊ #12622 |
636 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=eh,b^a=bd,c^a=ch,f^a=fg,i^a=i^3,d^b=dg,g^b=gh,i^c=i^2,f^d=fh,i^e=i^459 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2121, #72242930, #72242941 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2121, #72242930, #72242941 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096071);