Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C5 |
| direct product | C3×C37×C3⋊#1039 |
| unambiguous semidirect product | C3⋊(C3×C37×#1039) |
| derived | C3×C52 ⋊ C3×C4×C37 |
| Hall | C32×C52×C37 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C32×C37 ⋊ #1039 |
| Hall | C32×C52 ⋊ C4×C37 |
| Sylow | C52 ⋊ C3×Dic3×C37 |
| Sylow | C32 ⋊ C37×#1039 |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11100 |
8658 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 402);