Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D23×#4294 |
| unambiguous semidirect product | C23⋊(C22×#4294) |
| unambiguous semidirect product | (C2×C23)⋊(C2×#4294) |
| derived, Hall | C19×C23 ⋊ C22×C9 |
| Hall | C23×#4294 ⋊ C22 |
| Hall | C2×C19×D23 ⋊ C9 |
| Sylow | C23 ⋊ C22×#4294 |
| Sylow | C19 ⋊ C2×C9×D23 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7866 |
702 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 17);