Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C16 · Schur multiplier (H2) = C43 |
| direct product | C4×C16×AGL(1,𝔽5) |
| Fitting | C4×C5×C16 ⋊ C4 |
| derived, Sylow | C5 ⋊ C42×C16 |
558 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1095658);