Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D5×D169 |
| Fitting, Hall | C5×C9×C169 ⋊ C22 |
| derived, Hall | C5×C169 ⋊ C22×C9 |
| Hall | C9×C169 ⋊ C2×D5 |
| Sylow | C169 ⋊ C2×C9×D5 |
| Hall | C5×C9 ⋊ C2×D169 |
| Sylow | C5 ⋊ C2×C9×D169 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 36);