Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
| unambiguous semidirect product | D5⋊#1455 |
| Sylow | C5 ⋊ C2×#1455 |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,e^2=g,f^2=h,c^a=cg,i^a=i^2,c^b=ch,i^d=i^4,i^e=i^4152 conjugacy classes — view the full character table.
| maximal subgroup of | #72221173, #72221434, #72221440, … |
| maximal normal subgroup of | #72221434, #72221440, AGL(1,𝔽5)×#1455, … |
| maximal quotient of | #72221173 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1099370);