Finite Group DatabasebetaFinite Group Databasebeta| order | 31790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D55×C289 |
| unambiguous semidirect product | C5⋊(D11×C289) |
| unambiguous semidirect product | C11⋊(D5×C289) |
| Fitting, Hall | C5×C11×C289 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C2×C289 |
| Hall | C11×C289 ⋊ D5 |
| Hall | C5×C289 ⋊ D11 |
| Sylow | C11 ⋊ D5×C289 |
| Sylow | C5 ⋊ D11×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D55 |
| commutator, hypocenter | C5×C11 | C2×C289 |
| Frattini | C17 | C17×D55 |
| Fitting | C5×C11×C289 | C2 |
| socle, cosocle | C5×C11×C17 | C2×C17 |
| prime radical | C17×D55 | C17 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C289 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15895 |
8381 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31790, 11);