Finite Group DatabasebetaFinite Group Databasebeta| order | 31790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D935 |
| unambiguous semidirect product | C5⋊(C17×D187) |
| unambiguous semidirect product | C11⋊(C17×D85) |
| unambiguous semidirect product | C17⋊(C17×D55) |
| Fitting, socle, Hall | C5×C11×C172 ⋊ C2 |
| derived | C5×C11×C17 ⋊ C2×C17 |
| Hall | C11×C172 ⋊ D5 |
| Hall | C5×C172 ⋊ D11 |
| Sylow | C172 ⋊ D55 |
| Hall | C5×C11 ⋊ C17×D17 |
| Sylow | C11 ⋊ C17×D85 |
| Sylow | C5 ⋊ C17×D187 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D935 |
| commutator, cosocle, hypocenter | C5×C11×C17 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C172 | C2 |
| LCS | G ▷ C5×C11×C17 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1870 |
7973 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31790, 29);