Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×Dic111 |
| unambiguous semidirect product | C3⋊(C3×C52×Dic37) |
| derived | C3×C37 ⋊ C3×C4×C52 |
| Hall | C32×C52×C37 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C32×C37 ⋊ C4×C52 |
| Hall | C32×C52 ⋊ Dic37 |
| Sylow | C37 ⋊ C3×C52×Dic3 |
| Sylow | C32 ⋊ C52×Dic37 |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11100 |
8550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 405);