Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D171⋊D23 |
| unambiguous semidirect product | D207⋊D19 |
| unambiguous semidirect product | D437⋊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 ⋊ D9×D19 |
| 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 | D57⋊D23 |
| socle | C3×C19×C23 | C2×D3 |
| LCS | G ▷ C9×C19×C23 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3933 |
Polycyclic presentation:
2^2,3,19,23,3|c^3=f^2,d^a=d^18,e^a=e^22,c^b=c^2f,d^b=d^18,f^b=f^21023 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 24);