Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×Dic57 |
| unambiguous semidirect product | C3⋊(C3×C23×Dic19) |
| derived | C3×C19 ⋊ C3×C4×C23 |
| Hall | C32×C19×C23 ⋊ C4 |
| Hall | C19×C23 ⋊ C3×Dic3 |
| Hall | C32×C23 ⋊ Dic19 |
| Hall | C32×C19 ⋊ C4×C23 |
| Sylow | C19 ⋊ C3×Dic3×C23 |
| Sylow | C32 ⋊ C23×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C23 | D57 |
| commutator, hypocenter | C3×C19 | C3×C4×C23 |
| Frattini | C2 | C3×C23×D57 |
| Fitting, socle, prime radical | C2×C32×C19×C23 | C2 |
| cosocle | C2×C3×C19 | C2×C3×C23 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C3×C23 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5244 |
4140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 53);