Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×C3⋊#63120 |
| unambiguous semidirect product | C3⋊(C3×C13×#63120) |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C4 |
| derived | C3×C5×C13 ⋊ C3×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 ⋊ C3×C13×Dic39 |
256 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 390 |
3159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 832);