Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C9⋊#3866 |
| unambiguous semidirect product | C9⋊(C52×#3866) |
| Fitting, Hall | C52×C9×C37 ⋊ C4 |
| derived, Hall | C9×C37 ⋊ C4×C52 |
| Hall | C52×C37 ⋊ Dic9 |
| Hall | C52×C9 ⋊ #3866 |
| Sylow | C37 ⋊ C52×Dic9 |
| Sylow | C9 ⋊ C52×#3866 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
2325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 292);