Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#20258750 |
| derived, Hall | #13095201 ⋊ C4×C5 |
| Hall | C5×#13095201 ⋊ C4 |
| Hall | C5×C132 ⋊ Dic9 |
| Sylow | C132 ⋊ C5×Dic9 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2340 |
1080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 174);