Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D5×AΣL(1,𝔽16) |
| Fitting | C2×C5×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C5 ⋊ C22×AΣL(1,𝔽16) |
2774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#12753, C2×AGL(1,𝔽5)×AΣL(1,𝔽16), #72242710, … |
| maximal normal subgroup of | D5×#12753, D5×#33551, C2×AGL(1,𝔽5)×AΣL(1,𝔽16), … |
| maximal quotient of | D5×#12687 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 322277);