Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | D5⋊#2970 |
| Sylow | C5 ⋊ C2×#2970 |
2254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=g,d^2=f,g^2=h,b^a=bf,d^a=dh,i^a=i^3,d^c=dh,i^c=i^2,i^e=i^4,i^g=i^4140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2970, #72269233 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2970, #72269233 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1115143);