Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C19⋊#157 |
| unambiguous semidirect product | C19⋊(C23×#157) |
| Fitting, socle, Hall | C32×C19×C23 ⋊ C4 |
| derived, Hall | C32×C19 ⋊ C4×C23 |
| Hall | C19×C23 ⋊ #157 |
| Hall | C32×C23 ⋊ Dic19 |
| Sylow | C19 ⋊ C23×#157 |
| Sylow | C32 ⋊ C23×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C19⋊#157 |
| commutator, hypocenter | C32×C19 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C23 | C4 |
| prime radical | C3⋊D3×C19×C23 | C2 |
| cosocle | C3⋊D3×C19 | C2×C23 |
| LCS | G ▷ C32×C19 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2622 |
1380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 106);