Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×C9⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C9⋊(C132×AGL(1,𝔽5)) |
| Fitting, Hall | C5×C9×C132 ⋊ C4 |
| derived, Hall | C5×C9 ⋊ C4×C132 |
| Hall | C9×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ Dic9 |
| Sylow | C9 ⋊ C132×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C132×Dic9 |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3549 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 340);