Finite Group DatabasebetaFinite Group Databasebeta| order | 36686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D1411 |
| unambiguous semidirect product | C17⋊(C13×D83) |
| unambiguous semidirect product | C83⋊(C13×D17) |
| Fitting, socle, Hall | C13×C17×C83 ⋊ C2 |
| derived, Hall | C17×C83 ⋊ C2×C13 |
| Hall | C13×C83 ⋊ D17 |
| Hall | C13×C17 ⋊ D83 |
| Sylow | C83 ⋊ C13×D17 |
| Sylow | C17 ⋊ C13×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D1411 |
| commutator, cosocle, hypocenter | C17×C83 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C83 | C2 |
| LCS | G ▷ C17×C83 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18343 |
9191 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36686, 4);