Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C5×#15690149 |
| derived, Sylow | C132 ⋊ C22×C5×C9 |
| Hall | C5×#13095201 ⋊ C22 |
| Hall | C2×C5×C13⋊D13 ⋊ C9 |
| Hall | #13095201 ⋊ C22×C5 |
| Hall | C5×C132 ⋊ C22×C9 |
| Hall | C2×C13⋊D13 ⋊ C5×C9 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
1020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 292);