Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊Dic507 |
| unambiguous semidirect product | C3⋊(C5×Dic507) |
| derived, Hall | C32×C169 ⋊ C4×C5 |
| Hall | C32×C5×C169 ⋊ C4 |
| Hall | C5×C169 ⋊ C3⋊Dic3 |
| Sylow | C169 ⋊ C5×C3⋊Dic3 |
| Hall | C32×C5 ⋊ Dic169 |
| Sylow | C32 ⋊ C5×Dic169 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30420 |
7620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 70);