Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| unambiguous semidirect product | D5⋊#2883 |
| Fitting | C2×C5×H(5,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ C2×#2883 |
5338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^a=bf,f^a=fh,i^a=i^2,g^b=gh,d^c=dh,i^e=i^4,i^g=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #72253755, #72253762, AGL(1,𝔽5)×#2883, … |
| maximal normal subgroup of | #72253755, #72253762, AGL(1,𝔽5)×#2883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114717);