Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C9⋊#63120 |
| unambiguous semidirect product | C9⋊(C13×#63120) |
| Fitting, Hall | C5×C9×C132 ⋊ C4 |
| derived | C5×C9×C13 ⋊ C4×C13 |
| Hall | C9×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ Dic9 |
| Sylow | C132 ⋊ C9⋊AGL(1,𝔽5) |
| Hall | C5×C9 ⋊ C13×Dic13 |
| Sylow | C9 ⋊ C13×#63120 |
| Sylow | C5 ⋊ C13×Dic117 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
3081 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 343);