Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×C41×D25 |
| unambiguous semidirect product | C25⋊(C22×C9×C41) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C9×C41) |
| Fitting | C2×C9×C25×C41 ⋊ C2 |
| derived, Sylow | C25 ⋊ C22×C9×C41 |
| Hall | C9×C25×C41 ⋊ C22 |
| Hall | C25×C41 ⋊ C22×C9 |
| Hall | C9×C25 ⋊ C22×C41 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18450 |
10332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 47);