Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(#4294⋊C4) |
| unambiguous semidirect product | #4294⋊Dic23 |
| derived, Hall | C19×C23 ⋊ C4×C9 |
| Hall | C23×#4294 ⋊ C4 |
| Hall | Dic437 ⋊ C9 |
| Hall | #4294 ⋊ Dic23 |
| Sylow | C23 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C9×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C23⋊(D19⋊C3) |
| commutator, hypocenter | C19×C23 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C19×C23 | C2×C3 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15732 |
Polycyclic presentation:
2,3,19,23,2,3|a^2=e,b^3=f,c^a=c^18,d^a=d^22,c^b=c^7648 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 12);