Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C5 ⋊ #13346 |
1022 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 79 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|d^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fgh,i^a=i^4,c^b=cf,d^b=dh,g^b=gh,i^b=i^4,d^c=dg,f^d=fh83 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 88527);