Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D5⋊#2127 |
| Fitting | C5×#535 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2127 |
1510 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,e^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^2,c^b=ch,e^b=eh,f^b=fgh,i^d=i^4,f^e=fh,i^f=i^468 conjugacy classes — view the full character table.
| maximal subgroup of | #72221422, #72221463, AGL(1,𝔽5)×#2127, … |
| maximal normal subgroup of | #72221422, #72221463, AGL(1,𝔽5)×#2127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113513);