Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic2535 |
| unambiguous semidirect product | C3⋊(C3×Dic845) |
| derived | C3×C5×C169 ⋊ C3×C4 |
| Hall | C32×C5×C169 ⋊ C4 |
| Hall | C32×C169 ⋊ Dic5 |
| Hall | C5×C169 ⋊ C3×Dic3 |
| Sylow | C169 ⋊ C3×Dic15 |
| Hall | C32×C5 ⋊ Dic169 |
| Sylow | C32 ⋊ Dic845 |
| Sylow | C5 ⋊ C3×Dic507 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10140 |
7614 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 68);