Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×C3⋊(C3⋊#63120) |
| unambiguous semidirect product | C3⋊(C13×C3⋊#63120) |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C4 |
| derived | C32×C5×C13 ⋊ C4×C13 |
| Hall | C32×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ C3⋊Dic3 |
| Sylow | C132 ⋊ C3⋊ΓL(1,𝔽16) |
| Hall | C32×C5 ⋊ C13×Dic13 |
| Sylow | C32 ⋊ C13×#63120 |
| Sylow | C5 ⋊ C13×C3⋊Dic39 |
288 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, 892);