Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C5 |
| direct product | Dic3×C37×C52⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C37×C52⋊C3) |
| unambiguous semidirect product | (C52×Dic3)⋊(C3×C37) |
| derived | C3×C52 ⋊ C3×C4×C37 |
| Hall | C3×C37×C52⋊C3 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C3×C52⋊C3 ⋊ C4×C37 |
| Sylow | C52 ⋊ C3×Dic3×C37 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
2442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 388);