Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×#26012791 |
| derived, Hall | C52×C37 ⋊ C32×C4 |
| Hall | C3×C37×C52⋊C3 ⋊ C4 |
| Hall | #16814867 ⋊ C32 |
| Hall | C3×C52⋊C3 ⋊ Dic37 |
| Sylow | C37 ⋊ C3×#1039⋊C3 |
| Sylow | C52 ⋊ C32×Dic37 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
1248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 373);