Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C27×C4 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊#95 |
| Fitting | C2×C5×#95 ⋊ C4 |
| Sylow | C5 ⋊ #7554 |
3158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=h,b^a=bd,c^a=ce,i^b=i^2,i^g=i^4152 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1437, #72258341, #72258371 |
| maximal normal subgroup of | AGL(1,𝔽5)×#1437, #72258341, #72258371 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084874);