Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic23×#4296 |
| unambiguous semidirect product | C23⋊(C4×#4296) |
| derived, Hall | C19×C23 ⋊ C4×C9 |
| Hall | C23×#4296 ⋊ C4 |
| Hall | C19×Dic23 ⋊ C9 |
| Sylow | C23 ⋊ C4×#4296 |
| Sylow | C19 ⋊ C9×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D23×#4296 |
| commutator, hypocenter | C19×C23 | C4×C9 |
| Fitting, socle | C2×C19×C23 | C2×C9 |
| prime radical, cosocle | C2×C23×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1748 |
286 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 38);