Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C23⋊AGL(1,𝔽19) |
| unambiguous semidirect product | (C2×C23)⋊AGL(1,𝔽19) |
| unambiguous semidirect product | (C2×#4296)⋊D23 |
| Fitting, socle | C2×C19×C23 ⋊ C2×C9 |
| derived, Hall | C19×C23 ⋊ C22×C9 |
| Hall | C23×#4296 ⋊ C22 |
| Hall | C2×D437 ⋊ C9 |
| Hall | #4296 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×AGL(1,𝔽19) |
| Sylow | C19 ⋊ C2×C9×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C23⋊AGL(1,𝔽19) |
| commutator, hypocenter | C19×C23 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C23 | C2×C9 |
| prime radical | C2×C23⋊(D19⋊C3) | C3 |
| cosocle | C23×C19⋊C3 | C22×C3 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 874 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 62);