Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | AGL(1,𝔽5)×#550 |
| Fitting | C5×#550 ⋊ C4 |
| Sylow | C5 ⋊ C4×#550 |
3420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3498, #550×#1043 |
| maximal normal subgroup of | AGL(1,𝔽5)×#3498 |
| maximal quotient of | #550×#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114271);