Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D171 |
| unambiguous semidirect product | (C9×D23)⋊D19 |
| unambiguous semidirect product | (C19×D23)⋊D9 |
| Fitting, derived, Hall | C9×C19×C23 ⋊ C22 |
| Hall | C19×C23 ⋊ C2×D9 |
| Hall | C9×C23 ⋊ C2×D19 |
| Hall | C9×C19 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D171 |
| Sylow | C19 ⋊ D9×D23 |
| Sylow | C9 ⋊ D19×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C19×C23 | C22 |
| Frattini | C3 | D23×D57 |
| socle | C3×C19×C23 | C2×D3 |
| LCS | G ▷ C9×C19×C23 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3933 |
1131 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 20);