Finite Group DatabasebetaFinite Group Databasebeta| order | 20418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×AGL(1,𝔽83) |
| unambiguous semidirect product | D83⋊(C3×C41) |
| unambiguous semidirect product | (C3×D83)⋊C41 |
| unambiguous semidirect product | (C83⋊C41)⋊(C2×C3) |
| Fitting, socle, Hall | C3×C83 ⋊ C2×C41 |
| derived, Sylow | C83 ⋊ C2×C3×C41 |
| Hall | C3×C83⋊C41 ⋊ C2 |
| Hall | C83⋊C41 ⋊ C2×C3 |
| Hall | C3×D83 ⋊ C41 |
| Hall | D83 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽83) |
| commutator, cosocle, hypocenter | C83 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C83 | C2×C41 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 249 |
249 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20418, 10);