Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C529⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C529⋊(C3×AGL(1,𝔽5)) |
| Fitting, Hall | C3×C5×C529 ⋊ C4 |
| derived, Hall | C5×C529 ⋊ C3×C4 |
| Hall | C3×C529 ⋊ AGL(1,𝔽5) |
| Sylow | C529 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ Dic529 |
| Sylow | C5 ⋊ C3×Dic529 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
3183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 11);