Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#24926250 |
| Fitting, Hall | C3×C25×C109 ⋊ C4 |
| derived, Hall | C25×C109 ⋊ C3×C4 |
| Hall | C3×C109 ⋊ Dic25 |
| Sylow | C109 ⋊ C3×Dic25 |
| Hall | C3×C25 ⋊ #89137 |
| Sylow | C25 ⋊ C3×#89137 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
2109 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 29);