Finite Group DatabasebetaFinite Group Databasebeta| order | 31790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C5⋊(C11⋊(C17⋊D17)) |
| unambiguous semidirect product | C11⋊(C5⋊(C17⋊D17)) |
| unambiguous semidirect product | C17⋊D935 |
| Fitting, socle, derived, Hall | C5×C11×C172 ⋊ C2 |
| Hall | C11×C172 ⋊ D5 |
| Hall | C5×C172 ⋊ D11 |
| Sylow | C172 ⋊ D55 |
| Hall | C5×C11 ⋊ C17⋊D17 |
| Sylow | C11 ⋊ C5⋊(C17⋊D17) |
| Sylow | C5 ⋊ C11⋊(C17⋊D17) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C172 | C2 |
| LCS | G ▷ C5×C11×C172 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15895 |
Polycyclic presentation:
2,5,11,17^2|b^a=b^4,c^a=c^10,d^a=d^16,e^a=e^167949 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31790, 30);