Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#89137⋊C3 |
| unambiguous semidirect product | #89137⋊(C3×C25) |
| unambiguous semidirect product | (C25×#89137)⋊C3 |
| Fitting, Hall | C25×C109 ⋊ C3×C4 |
| derived, Sylow | C109 ⋊ C3×C4×C25 |
| Hall | C25×#89137 ⋊ C3 |
| Hall | C25×C109⋊C3 ⋊ C4 |
| Hall | #89137 ⋊ C3×C25 |
| Hall | C109⋊C3 ⋊ C4×C25 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2725 |
525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 14);