Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×#66526⋊C2 |
| unambiguous semidirect product | #66526⋊(C22×C25) |
| unambiguous semidirect product | (C2×#66526)⋊(C2×C25) |
| Fitting | C2×C25×C37 ⋊ C2×C9 |
| derived, Sylow | C37 ⋊ C22×C9×C25 |
| Hall | C25×#66526 ⋊ C22 |
| Hall | C2×C25×D37 ⋊ C9 |
| Hall | C25×C37 ⋊ C22×C9 |
| Hall | #66526 ⋊ C22×C25 |
| Hall | C2×D37 ⋊ C9×C25 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1850 |
1000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 113);