Finite Group DatabasebetaFinite Group Databasebeta| order | 1640 |
| isoclinism | isoclinic class of #4223⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×#4223⋊C5 |
| unambiguous semidirect product | #4223⋊(C2×C5) |
| unambiguous semidirect product | (C2×#4223)⋊C5 |
| unambiguous semidirect product | (D41⋊C5)⋊C4 |
| Fitting, socle | C2×C41 ⋊ C4×C5 |
| derived, Sylow | C41 ⋊ C2×C4×C5 |
| Hall | C2×#4223 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #4223⋊C5 |
| commutator, hypocenter | C41 | C2×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41 | C4×C5 |
| prime radical | C2×D41⋊C5 | C2 |
| cosocle | D41 | C22×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 82 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽41), D3×#4223⋊C5, C22×#4223⋊C5, … |
| maximal normal subgroup of | C2×AGL(1,𝔽41), C22×#4223⋊C5, C4×#4223⋊C5, … |
| maximal quotient of | D3×#4223⋊C5, C22×#4223⋊C5, C4×#4223⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1640, 48);