Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D5⋊#1884 |
| Fitting | C5×#532 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1884 |
1794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=eg,e^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^3,e^b=eh,f^b=fh,g^b=gh,i^b=i^2,e^c=eh,g^c=gh,i^d=i^4,i^g=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1884, #72221462, #72221475, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1884, #72221462, #72221475 |
| maximal quotient of | #72221622, #72226495 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105214);