Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×(C3⋊D3)⋊D37 |
| unambiguous semidirect product | (C3⋊D3)⋊(C25×D37) |
| unambiguous semidirect product | D111⋊(D3×C25) |
| Fitting, Hall | C32×C25×C37 ⋊ C22 |
| derived, Hall | C32×C37 ⋊ C22×C25 |
| Hall | C25×C37 ⋊ D32 |
| Hall | C32×C25 ⋊ C2×D37 |
| Sylow | C37 ⋊ D32×C25 |
| Sylow | C32 ⋊ C2×C25×D37 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5550 |
2925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 178);