Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D5⋊AΣL(1,𝔽16) |
| unambiguous semidirect product | D5⋊(C2×AΣL(1,𝔽16)) |
| Fitting | C2×C5×#120 ⋊ C4 |
| Sylow | C5 ⋊ C22×AΣL(1,𝔽16) |
2774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #72221422, #72221463, C2×AGL(1,𝔽5)×AΣL(1,𝔽16), … |
| maximal normal subgroup of | #72221422, #72221463, C2×AGL(1,𝔽5)×AΣL(1,𝔽16), … |
| maximal quotient of | #72242730 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113452);