Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#1504 |
| Fitting | C5×#525 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1504 |
1834 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,c^2=h,e^2=h,b^a=be,c^a=cg,e^a=eg,i^a=i^2,e^b=eh,f^b=fgh,i^d=i^4,i^f=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1504, #72242867, #72242870 |
| maximal normal subgroup of | AGL(1,𝔽5)×#1504, #72242867, #72242870 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1100498);