Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1587 |
| unambiguous semidirect product | C3⋊(C5×Dic529) |
| unambiguous semidirect product | C529⋊(C5×Dic3) |
| derived, Hall | C3×C529 ⋊ C4×C5 |
| Hall | C3×C5×C529 ⋊ C4 |
| Hall | C5×C529 ⋊ Dic3 |
| Sylow | C529 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ Dic529 |
| Sylow | C3 ⋊ C5×Dic529 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31740 |
7950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 6);