Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1311 |
| unambiguous semidirect product | C3⋊(C3×Dic437) |
| unambiguous semidirect product | C23⋊(C3×Dic57) |
| derived | C3×C19×C23 ⋊ C3×C4 |
| Hall | C32×C19×C23 ⋊ C4 |
| Hall | C19×C23 ⋊ C3×Dic3 |
| Hall | C32×C23 ⋊ Dic19 |
| Hall | C32×C19 ⋊ Dic23 |
| Sylow | C23 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ C3×Dic69 |
| Sylow | C32 ⋊ Dic437 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1311 |
| commutator, hypocenter | C3×C19×C23 | C3×C4 |
| Frattini | C2 | C3×D1311 |
| Fitting, socle, prime radical | C2×C32×C19×C23 | C2 |
| cosocle | C2×C3×C19×C23 | C2×C3 |
| LCS | G ▷ C3×C19×C23 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5244 |
3942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 54);