Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D5⋊#1819 |
| Fitting | C22×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1819 |
3118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=e,b^a=be,c^a=cf,f^a=fh,i^a=i^2,g^c=gh,i^d=i^4,i^g=i^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104628);