Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#4296⋊C4 |
| unambiguous semidirect product | #4296⋊(C4×C23) |
| derived, Sylow | C19 ⋊ C4×C9×C23 |
| Hall | C23×#4296 ⋊ C4 |
| Hall | C23×Dic19 ⋊ C9 |
| Hall | C19×C23 ⋊ C4×C9 |
| Hall | #4296 ⋊ C4×C23 |
| Hall | Dic19 ⋊ C9×C23 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1748 |
874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 36);