Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(#4296⋊C4) |
| unambiguous semidirect product | #4296⋊Dic23 |
| derived, Hall | C19×C23 ⋊ C4×C9 |
| Hall | C23×#4296 ⋊ C4 |
| Hall | Dic437 ⋊ C9 |
| Hall | #4296 ⋊ Dic23 |
| Sylow | C23 ⋊ #4296⋊C4 |
| Sylow | C19 ⋊ C9×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊AGL(1,𝔽19) |
| commutator, hypocenter | C19×C23 | C4×C9 |
| Fitting, socle | C2×C19×C23 | C2×C9 |
| prime radical, cosocle | C2×C23×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1748 |
Polycyclic presentation:
2,3^2,19,23,2|a^2=f,b^3=c,d^a=d^18,e^a=e^22,d^b=d^4,d^c=d^7280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 37);