Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D5⋊#1343 |
| Fitting | C5×#392 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1343 |
1164 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 88 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,d^2=g,b^a=bd,d^a=df,f^a=fh,i^a=i^2,d^b=dg,e^b=efg,i^c=i^4,e^d=eh,i^e=i^468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1094282);