Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×C3⋊#1035 |
| unambiguous semidirect product | C3⋊(C3×C23×#1035) |
| Fitting, Hall | C32×C23×C25 ⋊ C4 |
| derived | C3×C25 ⋊ C3×C4×C23 |
| Hall | C23×C25 ⋊ C3×Dic3 |
| Hall | C32×C25 ⋊ C4×C23 |
| Hall | C32×C23 ⋊ #1035 |
| Sylow | C25 ⋊ C3×Dic3×C23 |
| Sylow | C32 ⋊ C23×#1035 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3450 |
1656 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 64);