Finite Group DatabasebetaFinite Group Databasebeta| order | 3280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽41) |
| Fitting, socle | C2×C41 ⋊ C5×C8 |
| derived, Sylow | C41 ⋊ C2×C5×C8 |
| Hall | C2×#66502 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽41) |
| commutator, hypocenter | C41 | C2×C5×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41 | C5×C8 |
| prime radical | C2×D41⋊C5 | C4 |
| cosocle | #4223 | C22×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
82 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.