Finite Group DatabasebetaFinite Group Databasebeta| order | 31086 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1413 |
| unambiguous semidirect product | C9⋊(C11×D157) |
| unambiguous semidirect product | C157⋊(C11×D9) |
| Fitting, Hall | C9×C11×C157 ⋊ C2 |
| derived, Hall | C9×C157 ⋊ C2×C11 |
| Hall | C11×C157 ⋊ D9 |
| Sylow | C157 ⋊ C11×D9 |
| Hall | C9×C11 ⋊ D157 |
| Sylow | C9 ⋊ C11×D157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1413 |
| commutator, cosocle, hypocenter | C9×C157 | C2×C11 |
| Frattini | C3 | C11×D471 |
| Fitting | C9×C11×C157 | C2 |
| socle | C3×C11×C157 | D3 |
| LCS | G ▷ C9×C157 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15543 |
7788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31086, 7);