Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C3 |
| direct product | C25×C23⋊#157 |
| unambiguous semidirect product | C23⋊(C25×#157) |
| Fitting, Hall | C32×C23×C25 ⋊ C4 |
| derived, Hall | C32×C23 ⋊ C4×C25 |
| Hall | C23×C25 ⋊ #157 |
| Hall | C32×C25 ⋊ Dic23 |
| Sylow | C23 ⋊ C25×#157 |
| Sylow | C32 ⋊ C25×Dic23 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3450 |
1800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 90);