Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×D9×C25×C41 |
| unambiguous semidirect product | C9⋊(C22×C25×C41) |
| unambiguous semidirect product | (C2×C9)⋊(C2×C25×C41) |
| Fitting | C2×C9×C25×C41 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C25×C41 |
| Hall | C9×C25×C41 ⋊ C22 |
| Hall | C9×C41 ⋊ C22×C25 |
| Hall | C9×C25 ⋊ C22×C41 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18450 |
12300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 45);