Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C3×C5 |
| direct product | C37×C3⋊#64480 |
| unambiguous semidirect product | C3⋊(C37×#64480) |
| Fitting, socle | C3×C52×C37 ⋊ Dic3 |
| derived, Hall | C3×C52⋊C3 ⋊ C4×C37 |
| Hall | C3×C37×C52⋊C3 ⋊ C4 |
| Hall | C52×C37 ⋊ C3⋊Dic3 |
| Sylow | C52 ⋊ C3⋊Dic3×C37 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
666 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 538);