Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic1025 |
| derived, Hall | C25×C41 ⋊ C4×C9 |
| Hall | C9×C25×C41 ⋊ C4 |
| Hall | C9×C41 ⋊ Dic25 |
| Hall | C9×C25 ⋊ Dic41 |
| Sylow | C41 ⋊ C9×Dic25 |
| Sylow | C25 ⋊ C9×Dic41 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36900 |
9252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 8);