Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C13 |
| direct product | C5×C3⋊#14523147 |
| unambiguous semidirect product | C3⋊(C5×#14523147) |
| Fitting, socle | C3×C5×C132 ⋊ C3×C4 |
| derived | C3×C132 ⋊ C3×C4×C5 |
| Hall | C3×C5×#92789 ⋊ C4 |
| Hall | C3×#92789 ⋊ C4×C5 |
| Hall | C5×C132 ⋊ C3×Dic3 |
| Sylow | C132 ⋊ C3×C5×Dic3 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 615);