Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C22×C42×C5 ⋊ 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^a=i^2,i^f=i^4176 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1437, #72221494, #72221500 |
| maximal normal subgroup of | AGL(1,𝔽5)×#1437, #72221494, #72221500 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084875);